A095293 Number of A095283-primes in range ]2^n,2^(n+1)].

0, 2, 1, 4, 4, 9, 14, 29, 52, 90, 167, 312, 577, 1072, 2026, 3776, 7177, 13585, 25726, 49125, 93569, 178735, 342381, 657180, 1262818, 2430501, 4684999, 9040931, 17470670, 33798206, 65455531, 126889351, 246216909

Offset: 1

Author

Antti Karttunen, Jun 04 2004

Keywords

• nonn

Comments

As expected, the ratio a(n)/A095292(n) seems to approach 2: 0, 0, 1, 4, 1.33333, 2.25, 1.55556, 2.07143, 2.26087, 1.91489, 1.89773, 2.05263, 1.95593, 1.98519, 2.01793, 1.95344, 2.00924, 1.99633, 1.99287, 2.0083, 2.00075, 1.99746, 1.99841, 1.99971, 2.00034, 2.00001, 2.00018, 1.99977, 1.99971, 1.99997, 2.00004, 1.99995, 2.00003

Links

• A. Karttunen and J. 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

a(n) = A036378(n)-A095292(n). Cf. A095005.

Programs

PARI

a(n)=my(s);forprime(p=2^n+1,2^(n+1), s+=valuation(p+1, 2)%2); s \\ Charles R Greathouse IV, Oct 09 2013