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
Links
- 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.
Programs
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Mathematica
a[n_] := Length[Select[Range[10^n-2], PrimeQ[#] && PrimeQ[#+2] && Mod[#,4] == 1 &]]; Array[a,10]
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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
Extensions
a(11)-a(12) from Amiram Eldar, Jun 03 2024