A137780 a(n) = 1 + 2^( prime(n + 1) - prime(n) ).

3, 5, 5, 17, 5, 17, 5, 17, 65, 5, 65, 17, 5, 17, 65, 65, 5, 65, 17, 5, 65, 17, 65, 257, 17, 5, 17, 5, 17, 16385, 17, 65, 5, 1025, 5, 65, 65, 17, 65, 65, 5, 1025, 5, 17, 5, 4097, 4097, 17, 5, 17, 65, 5, 1025, 65, 65, 65, 5, 65, 17, 5, 1025, 16385, 17, 5, 17, 16385, 65, 1025, 5

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

From M. F. Hasler, Apr 21 2009: (Start)

a(n) = 1 + 2^A001223(n).

A001223(n) = A001511([a(n)/2]) = A007814(a(n)-1)).

a(n) = 1+4^A028334(n) for n>1. (End)

Mathematica

Table[1 + 2^(Prime[n + 1] - Prime[n]), {n, 1, 50}] (* G. C. Greubel, Feb 23 2017 *)
1+2^#&/@Differences[Prime[Range[70]]] (* Harvey P. Dale, Feb 18 2023 *)

Prog

(PARI) a(n) = 1 + 2^( prime(n + 1) - prime(n) )
(Python)
from sympy import prime
def A137780(n): return 1+(1<<(prime(n+1)-prime(n))) # Chai Wah Wu, Jul 08 2022

Crossrefs

Sequence in context: A084041 A028254 A318351 * A079372 A055382 A165235

Adjacent sequences: A137777 A137778 A137779 * A137781 A137782 A137783

Keyword

nonn

Author

Alexander R. Povolotsky, Apr 28 2008

Extensions

Extended beyond a(30) by M. F. Hasler, Apr 21 2009

Status

approved