A073050 a(n) = prime(2^n + 2) - prime(2^n + 1) - 1.

1, 1, 5, 1, 1, 3, 5, 5, 3, 3, 9, 11, 5, 21, 1, 3, 23, 1, 31, 15, 17, 17, 15, 91, 9, 13, 9, 41, 43, 7, 97, 69, 7, 35, 7, 23, 5, 19, 63, 5, 35, 25, 21, 29, 29, 9, 117, 29, 3, 85, 119, 35, 37, 127, 9, 51, 5, 9, 47, 33, 49, 83, 83, 19, 41, 5, 17, 95, 3, 29, 29, 401, 25, 143, 19, 27, 65, 57

Offset

1,3

Comments

Total sum of the second differences of the primes (A036263) to 2^n.

Links

Table of n, a(n) for n=1..78.

Marek Wolf, Some conjectures on the gaps between consecutive primes

Mathematica

a[n_] := Prime[2^n+2]-Prime[2^n+1]-1; a/@Range[26]

Prog

(Python)
from sympy import nextprime, prime
def a(n): p = prime(2**n + 1); return nextprime(p) - p - 1
print([a(n) for n in range(1, 25)]) # Michael S. Branicky, Dec 27 2021

Crossrefs

Cf. A036263, A033844.

Sequence in context: A346916 A359667 A010129 * A366426 A154740 A179261

Adjacent sequences: A073047 A073048 A073049 * A073051 A073052 A073053

Keyword

nonn

Author

Robert G. Wilson v, Aug 15 2002

Extensions

a(42)-a(47) from Michael S. Branicky, Dec 27 2021

a(48)-a(78) from Michael S. Branicky, Dec 30 2021 using A033844

Status

approved