A092131 Distance from 2^n to the next prime.

0, 1, 3, 1, 5, 3, 3, 1, 9, 7, 5, 3, 17, 27, 3, 1, 29, 3, 21, 7, 17, 15, 9, 43, 35, 15, 29, 3, 11, 3, 11, 15, 17, 25, 53, 31, 9, 7, 23, 15, 27, 15, 29, 7, 59, 15, 5, 21, 69, 55, 21, 21, 5, 159, 3, 81, 9, 69, 131, 33, 15, 135, 29, 13, 131, 9, 3, 33, 29, 25, 11, 15, 29, 37, 33, 15, 11, 7, 23

Offset

1,3

Comments

Essentially the same as A013597. - T. D. Noe, Jul 17 2007

From Jianing Song, May 28 2024: (Start)

Not every odd number is present, as no term can be equal to a Sierpiński number (for example 78557); cf. A076336. See also A067760.

Conjecture: Every odd number which is not a Sierpiński number is a term. In other words, for every odd k which is not a Sierpiński number, there exists some n >= 1 such that 2^n + 1, 2^n + 3, ..., 2^n + (k-2) are all composite while 2^n + k is prime. (End)

Links

T. D. Noe, Table of n, a(n) for n=1..5000

Formula

a(n) = nextprime(2^n) - 2^n.

a(n) = A007920(A000079(n)). - Michel Marcus, Oct 19 2022

Example

a(13)=17 because 2^13=8192 and the next prime is 8209=8192+17.

Mathematica

Join[{0}, NextPrime[#]-#&/@(2^Range[2, 80])] (* Harvey P. Dale, Jun 06 2012 *)

Prog

(PARI) for(i=1, 100, x=2^i; print1(nextprime(x)-x, ", "))

Crossrefs

Cf. A013597.

Equivalent sequence for previous prime: A013603.

Cf. A000079, A007920, A067760, A076336.

Sequence in context: A340526 A161946 A013597 * A092099 A096567 A239626

Adjacent sequences: A092128 A092129 A092130 * A092132 A092133 A092134

Keyword

easy,nonn,changed

Author

Helmut Richter (richter(AT)lrz.de), Mar 30 2004

Status

approved