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Search: a057178 -id:a057178
Displaying 1-10 of 17 results found. page 1 2
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A126856 Numbers n such that (31^n + 1)/32 is prime. +10
13
109, 461, 1061, 50777 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(5) > 10^5. - Robert Price, Jul 12 2013
LINKS
Table of n, a(n) for n=1..4.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
Eric Weisstein's World of Mathematics, Repunit.
H. Lifchitz, Mersenne and Fermat primes field
MATHEMATICA
Do[ p=Prime[n]; If[ PrimeQ[ (31^p + 1)/32 ], Print[p] ], {n, 1, 1100} ]
PROG
(PARI) is(n)=isprime((31^n+1)/32) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382. Cf. A084741, A084742, A065507, A126659.
KEYWORD
bref,hard,more,nonn
AUTHOR
Alexander Adamchuk, Mar 23 2007
EXTENSIONS
a(4) from Robert Price, Jul 12 2013
STATUS
approved
A229145 Numbers k such that (36^k + 1)/37 is prime. +10
12
31, 191, 257, 367, 3061, 110503, 1145393 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All such numbers k are prime.
Note that a(6) = 110503 corresponds to (36^110503 + 1)/37, which is only a probable prime with 171975 digits.
The primes corresponding to the terms of this sequence have 1 as their last digit and an even number as their next-to-last digit. - Iain Fox, Dec 08 2017
LINKS
Table of n, a(n) for n=1..7.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.
MATHEMATICA
Do[ p=Prime[n]; If[ PrimeQ[ (36^p + 1)/37 ], Print[p] ], {n, 1, 9592} ]
PROG
(PARI) is(n)=isprime((36^n+1)/37) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240.
KEYWORD
hard,more,nonn
AUTHOR
Robert Price, Sep 15 2013
EXTENSIONS
a(6) = 110503 (posted by Lelio R. Paula on primenumbers.net) from Paul Bourdelais, Dec 08 2017
a(7) from Paul Bourdelais, Nov 03 2023
STATUS
approved
A185240 Numbers k such that (35^k + 1)/36 is prime. +10
11
11, 13, 79, 127, 503, 617, 709, 857, 1499, 3823, 135623, 280979 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes. a(11) > 10^5.
LINKS
Table of n, a(n) for n=1..12.
Paul Bourdelais, A Generalized Repunit Conjecture
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit
MATHEMATICA
Do[ p=Prime[n]; If[ PrimeQ[ (35^p + 1)/36 ], Print[p] ], {n, 1, 9592} ]
PROG
(PARI) is(n)=isprime((35^n+1)/36) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382. Cf. A084741, A084742, A065507, A126659, A126856.
KEYWORD
hard,more,nonn
AUTHOR
Robert Price, Aug 29 2013
EXTENSIONS
a(11)=135623 found as probable prime and added by Paul Bourdelais, Jul 05 2018
a(12) from Paul Bourdelais, Sep 13 2021
STATUS
approved
A229524 Numbers k such that (38^k + 1)/39 is prime. +10
8
5, 167, 1063, 1597, 2749, 3373, 13691, 83891, 131591 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes. a(9) > 10^5.
LINKS
Table of n, a(n) for n=1..9.
P. Bourdelais, A Generalized Repunit Conjecture
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.
MATHEMATICA
Do[ p=Prime[n]; If[ PrimeQ[ (38^p + 1)/39 ], Print[p] ], {n, 1, 9592} ]
PROG
(PARI) is(n)=ispseudoprime((38^n+1)/39) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145.
KEYWORD
hard,more,nonn
AUTHOR
Robert Price, Sep 25 2013
EXTENSIONS
a(9)=131591 corresponds to a probable prime discovered by Paul Bourdelais, Jul 03 2018
STATUS
approved
A213216 Numbers n such that (12^n + 11^n)/23 is prime. +10
6
47, 401, 509, 8609 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are prime.
a(5) > 10^5.
LINKS
Table of n, a(n) for n=1..4.
MATHEMATICA
Select[ Prime[ Range[1, 100000] ], PrimeQ[ (12^# + 11^#)/23 ]& ]
PROG
(PARI) is(n)=ispseudoprime((12^n+11^n)/23) \\ Charles R Greathouse IV, Feb 20 2017
CROSSREFS
Cf. A057178, A128341, A181141, A187819, A217095.
KEYWORD
hard,nonn,more
AUTHOR
Robert Price, Mar 02 2013
EXTENSIONS
Removed incorrect first term of "2".
STATUS
approved
A229663 Numbers n such that (40^n + 1)/41 is prime. +10
6
53, 67, 1217, 5867, 6143, 11681, 29959 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(8) > 10^5.
LINKS
Table of n, a(n) for n=1..7.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.
MATHEMATICA
Do[ p=Prime[n]; If[ PrimeQ[ (40^p + 1)/41 ], Print[p] ], {n, 1, 9592} ]
PROG
(PARI) is(n)=ispseudoprime((40^n+1)/41) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524.
KEYWORD
hard,more,nonn
AUTHOR
Robert Price, Sep 27 2013
STATUS
approved
A230036 Numbers n such that (39^n + 1)/40 is prime. +10
6
3, 13, 149, 15377 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(5) > 10^5.
LINKS
Table of n, a(n) for n=1..4.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.
MATHEMATICA
Do[ p=Prime[n]; If[ PrimeQ[ (39^p + 1)/40 ], Print[p] ], {n, 1, 9592} ]
PROG
(PARI) is(n)=ispseudoprime((39^n+1)/40) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A000978 (numbers n such that (2^n + 1)/3 is prime).
Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524.
KEYWORD
hard,more,nonn
AUTHOR
Robert Price, Oct 05 2013
STATUS
approved
A231604 Numbers n such that (42^n + 1)/43 is prime. +10
5
3, 709, 1637, 17911, 127609, 172663 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The first 5 terms are primes.
LINKS
Table of n, a(n) for n=1..6.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
P. Bourdelais, A Generalized Repunit Conjecture
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.
MATHEMATICA
Do[ p=Prime[n]; If[ PrimeQ[ (42^p + 1)/43 ], Print[p] ], {n, 1, 9592} ]
PROG
(PARI) is(n)=ispseudoprime((42^n+1)/43) \\ Charles R Greathouse IV, Feb 20 2017
CROSSREFS
Cf. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524, A230036, A229663.
KEYWORD
hard,more,nonn
AUTHOR
Robert Price, Nov 11 2013
EXTENSIONS
a(5)=127609 corresponds to a probable prime discovered by Paul Bourdelais, Jul 02 2018
a(6)=172663 corresponds to a probable prime discovered by Paul Bourdelais, Jul 29 2019
STATUS
approved
A185239 Numbers n such that (11^n + 10^n)/21 is prime. +10
4
53, 421, 647, 1601, 35527 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are prime.
a(6) > 10^5.
LINKS
Table of n, a(n) for n=1..5.
MATHEMATICA
Select[ Prime[ Range[1, 100000] ], PrimeQ[ (11^# + 10^#)/21 ]& ]
PROG
(PARI) is(n)=ispseudoprime((11^n+10^n)/21) \\ Charles R Greathouse IV, May 22 2017
CROSSREFS
Cf. A057178, A128341, A181141, A187819, A217095, A213216.
KEYWORD
nonn,more
AUTHOR
Robert Price, Apr 05 2013
STATUS
approved
A231865 Numbers n such that (43^n + 1)/44 is prime. +10
4
5, 7, 19, 251, 277, 383, 503, 3019, 4517, 9967, 29573 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(11) > 10^5.
LINKS
Table of n, a(n) for n=1..11.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.
MATHEMATICA
Do[ p=Prime[n]; If[ PrimeQ[ (43^p + 1)/44 ], Print[p] ], {n, 1, 9592} ]
PROG
(PARI) is(n)=ispseudoprime((43^n+1)/44) \\ Charles R Greathouse IV, Feb 20 2017
CROSSREFS
Cf. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524, A230036, A229663, A231604.
KEYWORD
hard,more,nonn
AUTHOR
Robert Price, Nov 14 2013
STATUS
approved
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Last modified September 15 06:53 EDT 2024. Contains 375931 sequences. (Running on oeis4.)