A095006 Number of evil primes (A027699) in range ]2^n,2^(n+1)].

1, 1, 0, 3, 2, 5, 4, 23, 27, 62, 95, 222, 367, 777, 1269, 2910, 4859, 10140, 17714, 36714, 66020, 133400, 245959, 493532, 916913, 1822087, 3428633, 6782008, 12870735, 25339113, 48419194, 95194890, 182818705, 358637144, 691891351, 1355985684, 2625053871, 5142673207

Offset: 1

Author

Antti Karttunen and Labos Elemer, Jun 01 2004

Keywords

• nonn

Examples

			From _Michael De Vlieger_, Feb 27 2017: (Start)
a(2) = 1 since between 2^2 and 2^3 only the prime 5 (binary 11) has an even number of 1s.
a(3) = 0 since none of the primes between 2^3 and 2^4 have an even number of 1s in their binary expansions.
a(4) = 3 since the primes 17, 23, and 29 have an even number of 1s in their binary expansions (i.e., 10001, 10111, 11101). (End)
		

Links

• 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)].

Crossrefs

Cf. A027699, A036378, A095005.

Programs

Mathematica

Table[m = Count[Prime@ Range[PrimePi[2^n] + 1, PrimePi[2^(n + 1) - 1]], k_ /; EvenQ@ DigitCount[k, 2, 1]]; Print@ m; m, {n, 24}] (* Michael De Vlieger, Feb 27 2017 *)

Formula

a(n) = A036378(n) - A095005(n).

Extensions

a(34)-a(38) from Amiram Eldar, Jun 20 2024