A083556 n-th Payam number E_{+}(n), defined as the smallest positive odd integer k such that for every positive integer n, the number k*2^n+1 is not divisible by any primes p such that the multiplicative order of 2 mod p is less than or equal to e.

3, 9, 15, 105, 105, 105, 105, 105, 165, 165, 75075, 75075, 75075, 75075, 75075, 75075, 855855, 855855, 5583435, 5583435, 5583435, 18625035, 18625035, 18625035, 18625035, 18625035, 27183585, 27183585, 27183585, 27183585, 27183585

Offset

2,1

Comments

Payam numbers are good candidates for looking for Proth primes, i.e. primes of the form k*2^n+1

Links

Table of n, a(n) for n=2..32.

Author?, Title?

Eric Weisstein's World of Mathematics, Payam Number

Example

E_{+}(3) = 9 because 9 is the smallest odd integer k such that for every nonnegative integer n, k*2^n+1 is not divisible by 3 or 7, the only primes p for which the multiplicative order of 2 mod p is less than or equal to 3.

Crossrefs

Cf. A080076.

Cf. A083391.

Sequence in context: A348199 A242438 A355716 * A015664 A272621 A134137

Adjacent sequences: A083553 A083554 A083555 * A083557 A083558 A083559

Keyword

hard,nonn

Author

David Terr, Jun 10 2003

Status

approved