OFFSET
1,2
FORMULA
Generate the prime sequence with primes labeled 1 mod 4 or 3 mod 4. Add count of primes to sequence if just one prime occurs before interruption by a prime congruent to 3 mod 4.
EXAMPLE
a(3)=31 because 31 single primes occur below 10^3, each interrupted in the run by a prime congruent to 3 mod 4.
MATHEMATICA
A002144= Select[4 Range[0, 10^4] + 1, PrimeQ[#] &];
A002145= Select[4 Range[0, 10^4] + 3, PrimeQ[#] &];
lst = {}; Do[If[Length[s = Select[A002144,Between[{A002145[[i]],A002145[[i + 1]]}]]] == 1, AppendTo[lst, Last[s]]], {i, Length[A002145] - 1}]; Table[Count[lst, x_ /; x < 10^n], {n, 4}] (*Robert Price,May 31 2019 *)
PROG
(PARI) a(n)=my(p=2, q=3, t); forprime(r=5, nextprime(10^n), if(q%4==1&&p%4==3&&r%4==3, t++); p=q; q=r); t \\Charles R Greathouse IV,Sep 30 2011
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Enoch Haga,Mar 02 2004
EXTENSIONS
a(9) fromCharles R Greathouse IV,Sep 30 2011
a(10)-a(11) fromChai Wah Wu,Mar 18 2018
STATUS
approved