A369109 a(n) is the number of pairs of twin primes p and p+2 both less than or equal to 10^n such that p is congruent to 1 modulo 4.

1, 4, 19, 105, 604, 4046, 29482, 220419, 1712731, 13706592, 112196635, 935286453

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Gareth A. Jones and Alexander K. Zvonkin, A number-theoretic problem concerning pseudo-real Riemann surfaces, arXiv:2401.00270 [math.NT], 2023. See Table 4 at page 13.

Mathematica

a[n_] := Length[Select[Range[10^n-2], PrimeQ[#] && PrimeQ[#+2] && Mod[#, 4] == 1 &]]; Array[a, 10]

Prog

(PARI) lista(nmax) = {my(prev = 2, c = 0, pow = 10, n = 1, nm = nmax + 1); forprime(p = 3, , if(p > pow, print1(c, ", "); pow *= 10; n++; if(n == nm, break)); if(prev % 4 == 1 && p == prev + 2, c++); prev = p); } \\ Amiram Eldar, Jun 03 2024

Crossrefs

Cf. A001097, A001359, A004613, A006512, A007508, A369105, A369107, A369108, A369111.

Sequence in context: A367239 A062265 A088129 * A082030 A348802 A052751

Adjacent sequences: A369106 A369107 A369108 * A369110 A369111 A369112

Keyword

nonn,more,changed

Author

Stefano Spezia, Jan 13 2024

Extensions

a(11)-a(12) from Amiram Eldar, Jun 03 2024

Status

approved