A339580 -id:A339580 - cp's OEIS frontend

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

N. J. A. Sloane, Dec 24 2020

nonn

Conjectured to grow without limit.

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

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

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.

See A339580 for records.

Cf. A063377, A063378, A339581.

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

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

A339581 Indices of records in A063377.

Original entry on oeis.org

1, 2, 89, 1122659, 19099919, 85864769, 26089808579, 554688278429, 4090932431513069, 95405042230542329

Offset: 1

N. J. A. Sloane, Dec 24 2020

The records themselves begin 0,5,6,7,8,9,10,12,13,14.
a(11) <= 90616211958465842219 = A005602(15). Between a(10) and this upper bound could be another record which might not be listed in A005602.
a(n) == 9 mod 10 for n > 2 (see A063377). - Michael S. Branicky, Dec 24 2020

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

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.

Cf. A005602, A057331, A063377, A063378, A339579, A339580.

a(n) = A057331(n + 2) for n >= 2. - David A. Corneth, Dec 25 2020

a(6) corrected and a(7) found by David A. Corneth, Dec 24 2020.

a(8)-a(10) were taken from A057331 and the bound on a(11) was taken from A005602. - David A. Corneth and Amiram Eldar, Dec 25 2020

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

PARI

Formula