A095005 Number of odious primes (A027697) in range ]2^n,2^(n+1)].

0, 1, 2, 2, 5, 8, 19, 20, 48, 75, 160, 242, 505, 835, 1761, 2799, 5890, 10250, 20921, 36872, 74316, 134816, 267749, 492286, 977207, 1823657, 3598657, 6779899, 13336543, 25358424, 49763462, 95140695, 186504600, 358630024, 702300885, 1356118149, 2654709953, 5142968571

Offset: 1

Author

Antti Karttunen and Labos Elemer, Jun 01 2004

Keywords

• nonn

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. A027697, A036378, A095006.

Programs

Mathematica

Table[Count[Prime@ Range[PrimePi[2^n] + 1, PrimePi[2^(n + 1) - 1]], k_ /; OddQ@ First@ DigitCount[k, 2]], {n, 24}] (* Michael De Vlieger, Feb 25 2017 *)

PARI

a(n) = #select(x->((hammingweight(x)%2)==1),primes([2^n+1,2^(n+1)])); \\ Michel Marcus, Feb 26 2017

Formula

a(n) = A036378(n) - A095006(n).

Extensions

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