A095059 Number of primes with two 0-bits (A095079) in range ]2^n,2^(n+1)].

0, 0, 0, 1, 2, 4, 0, 9, 5, 14, 4, 16, 9, 18, 0, 21, 21, 21, 7, 41, 22, 31, 5, 37, 20, 33, 14, 37, 45, 47, 0, 69, 31, 36, 34, 55, 34, 71, 10, 60, 50, 69, 22, 81, 52, 59, 5, 97, 71, 79, 42, 67, 86, 95, 13, 103, 61, 81, 47, 98, 50, 110, 0, 108, 87, 116, 36, 125, 98, 98, 29, 126, 90, 125, 46, 107, 100, 125, 8, 158, 81, 109, 65, 156, 94, 131, 27, 127, 144, 146, 38, 167, 129, 137, 6, 127, 112, 178, 76

Offset

1,5

Links

Michael S. Branicky, Table of n, a(n) for n = 1..1000

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

Samuel S. Wagstaff, Jr., Prime Numbers with a fixed number of one bits or zero bits in their binary representation, Exp. Math. vol. 10, issue 2 (2001) 267, Table 4. - From N. J. A. Sloane, Jun 19 2011.

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

Prog

(Python)
from sympy import isprime
from itertools import combinations, count, islice
def a(n): # generator of terms
    if n < 2: return 0
    b, d = (1<<n+1)-1, n-1
    return sum(1 for i, j in combinations(range(d), 2) if isprime(b-(1<<(d-i))-(1<<(d-j))))
print([a(n) for n in range(1, 100)]) # Michael S. Branicky, Dec 27 2023

Crossrefs

Cf. A095018, A095056, A095057, A095058.

Sequence in context: A071607 A338620 A358645 * A021419 A338168 A180192

Adjacent sequences: A095056 A095057 A095058 * A095060 A095061 A095062

Keyword

base,nonn

Author

Antti Karttunen, Jun 01 2004

Extensions

Added terms a(34)-a(99) from the Wagstaff paper. - N. J. A. Sloane, Jun 19 2011

Status

approved