A095009 Number of 8k+1 primes (A007519) in range ]2^n,2^(n+1)].

0, 0, 0, 1, 1, 4, 4, 10, 18, 31, 64, 115, 216, 398, 752, 1413, 2692, 5092, 9642, 18355, 35089, 66907, 128431, 246479, 473201, 911650, 1756523, 3390156, 6551387, 12673576, 24545135, 47583812, 92329094, 179317195, 348545465, 678019818, 1319938243, 2571401536

Offset

1,6

Links

Table of n, a(n) for n=1..38.

Antti Karttunen and John Moyer, C-program for computing the initial terms of this sequence.

Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)].

Formula

a(n) = A095013(n) - A095012(n) = A095007(n) - A095011(n).

Mathematica

Table[Count[Range[2^n, 2^(n+1)], _?(PrimeQ[#]&&Mod[#, 8]==1&)], {n, 20}] (* Harvey P. Dale, Dec 19 2025 *)

Crossrefs

Cf. A007519, A091126, A095007, A095011, A095012, A095013.

Sequence in context: A050339 A087288 A185779 * A178820 A284784 A219803

Adjacent sequences: A095006 A095007 A095008 * A095010 A095011 A095012

Keyword

nonn

Author

Antti Karttunen and Labos Elemer, Jun 01 2004

Extensions

a(34)-a(38) from Amiram Eldar, Jun 12 2024

Status

approved