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

Author

N. J. A. Sloane, Dec 24 2020

Keywords

• nonn

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.

Crossrefs

See A339580 for records.

Cf. A063377, A063378, A339581.

Programs

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

Formula

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