A117835 - OEIS

A117835

Prime numbers for which the product of the digits is a noncomposite number.

2, 3, 5, 7, 11, 13, 17, 31, 71, 113, 131, 151, 211, 311, 1117, 1151, 1171, 1511, 2111, 11113, 11117, 11131, 11171, 11311, 111121, 111211, 112111, 113111, 131111, 311111, 511111, 1111151, 1111211, 1111711, 1117111, 1171111, 11111117, 11111131, 11111171, 11111311, 11113111, 11131111

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OFFSET

1,1

COMMENTS

None of the numbers in the sequence can have a digit 0, 4, 6, 8 or 9. The digits are all 1's, or there is one digit 2, 3, 5 or 7 and all the others are 1's.

A variant ofA046703where the "all '1's" (repunit primes R(k) with k inA004023:R(2) = 11, R(19),...) are excluded. -M. F. Hasler,Apr 22 2019

Contains primes inA028842as a subset. -M. F. Hasler,Apr 23 2019

LINKS

Table of n, a(n) for n=1..42.

FORMULA

A117835= { n inA008578|A007954(n) is again inA008578}. -M. F. Hasler,Apr 23 2019

MATHEMATICA

Select[Prime[Range[10^6]], PrimeQ[Times@@IntegerDigits[#]]||Times@@IntegerDigits[#]==1&] (*James C. McMahon,Sep 24 2024 *)

PROG

(PARI)

select( is_A117835(n)=isprime(n)&&(isprime(n=vecprod(digits(n)))||n==1), [0..999]) \\ In older PARI versions, vecprod=factorback. \\M. F. Hasler,Apr 23 2019

(PARI)

next_A117835(n)={until( isprime(n), my(d=digits(n)); n=if(n<3||Set(d)==[1], n+1, fromdigits(apply(t->if(t<2, 1, t<7, nextprime(t+1), 11), d)))); n}

A117835_vec(N=99)=vector(N, i, t=next_A117835(if(i>1, t))) \\M. F. Hasler,Apr 23 2019

CROSSREFS

Cf.A046703( "prime" variant),A007954(product of digits),A008578(noncomposite numbers),A028842(product of digits is prime).

Sequence in context:A186307 A321420 A118725*A120639 A141263 A016114

Adjacent sequences:A117832 A117833 A117834*A117836 A117837 A117838

KEYWORD

base,nonn

AUTHOR

Luc Stevens (lms022(AT)yahoo ), Apr 30 2006

EXTENSIONS

Name changed, following a remark fromZak Seidov,and edited byM. F. Hasler,Apr 22 2019

STATUS

approved