A339579 a(n) = least nonnegative integer k such that n*2^k - 1 is composite.

4, 3, 5, 2, 0, 4, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0

Offset

1,1

Comments

Conjectured to grow without limit.

A063377 is an essentially identical sequence, although with a slightly different definition, different initial terms, and different offset.

References

Carl Pomerance, Problem 81:21 (= 321), in R. K. Guy problem list.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

R. K. Guy, editor, Western Number Theory Problems, 1985-12-21 & 23, Typescript, Jul 13 1986, Dept. of Math. and Stat., Univ. Calgary, 11 pages. Annotated scan of pages 1, 3, 7, 9, with permission.

Formula

For n >= 3, a(n) = A063377(n-1).

Prog

(PARI) A339579(n) = for(k=0, oo, my(t=(n*(2^k))-1); if((t>1)&&!isprime(t), return(k))); \\ Antti Karttunen, Dec 24 2020

Crossrefs

See A339580 for records.

Cf. A063377, A063378, A339581.

Sequence in context: A274260 A011397 A352692 * A081665 A131911 A254037

Adjacent sequences: A339576 A339577 A339578 * A339580 A339581 A339582

Keyword

nonn

Author

N. J. A. Sloane, Dec 24 2020

Status

approved