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

Author

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

Keywords

• easy
• nonn

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)

Examples

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

Links

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

Crossrefs

Cf. A013597.

Equivalent sequence for previous prime: A013603.

Cf. A000079, A007920, A067760, A076336.

Programs

Mathematica

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

PARI

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

Formula

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

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