A092636 Number of consecutive prime runs of 1 prime congruent to 1 mod 4 below 10^n.

1, 5, 31, 208, 1555, 12465, 102704, 869060, 7540342, 66571720, 595513442

Offset: 1

Author

Enoch Haga, Mar 02 2004

Keywords

• more
• nonn

Examples

			a(3)=31 because 31 single primes occur below 10^3, each interrupted in the run by a prime congruent to 3 mod 4.
		

Crossrefs

Cf. A091318, A092637-A092665.

Programs

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 *)

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

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.

Extensions

a(9) from Charles R Greathouse IV, Sep 30 2011

a(10)-a(11) from Chai Wah Wu, Mar 18 2018