A086769 a(n) = Sum_{i=1..n} 2^(b(i) - 1), where b(n) is the differences between consecutive primes.

1, 3, 5, 13, 15, 23, 25, 33, 65, 67, 99, 107, 109, 117, 149, 181, 183, 215, 223, 225, 257, 265, 297, 425, 433, 435, 443, 445, 453, 8645, 8653, 8685, 8687, 9199, 9201, 9233, 9265, 9273, 9305, 9337, 9339, 9851, 9853, 9861, 9863, 11911, 13959, 13967, 13969

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

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

Example

2^(3-2)/2=1, so a(1)=1. 2^(5-3)/2=2, so a(2)=1+2=3.

Mathematica

Accumulate[2^(#-1)&/@Differences[Prime[Range[50]]]] (* Harvey P. Dale, Aug 10 2024 *)

Prog

(MATLAB) P = primes(500); l = length(P); S = P(2:l) - P(1:(l - 1)); A = cumsum(2.^(S-1))

Crossrefs

Cf. A001223.

Sequence in context: A396294 A137162 A293863 * A018753 A073217 A063484

Adjacent sequences: A086766 A086767 A086768 * A086770 A086771 A086772

Keyword

nonn,easy

Author

David G. Williams (davwill24(AT)aol.com), Aug 02 2003

Extensions

Edited by David Wasserman, Aug 28 2003

Status

approved