A083391 n-th Payam number E_{-}(n), defined as the smallest positive odd integer k such that for every positive integer m, the number k*2^m-1 is not divisible by any primes p such that the multiplicative order of 2 mod p is less than or equal to n.

3, 3, 45, 45, 45, 45, 45, 45, 2145, 2805, 92235, 92235, 92235, 92235, 92235, 92235, 529815, 529815, 529815, 529815, 529815, 529815, 529815, 529815, 1426425, 1426425, 247016055, 247016055, 247016055, 247016055

Offset

2,1

Comments

Payam numbers yield many primes of the form k*2^n+1 (Proth primes) and k*2^n-1.

Links

Table of n, a(n) for n=2..31.

Robert Smith, A coordinated search for primes in the Payam number series.

Eric Weisstein's World of Mathematics, Payam Number

Example

E_{-}(4) = 45 because 45 is the smallest odd integer k such that for every nonnegative integer m, k*2^m-1 is not divisible by 3, 5, or 7, the only primes p for which the multiplicative order of 2 mod p is less than or equal to 4.

Crossrefs

Cf. A083556.

Cf. A080076.

Sequence in context: A372423 A174325 A290366 * A165636 A142469 A009809

Adjacent sequences: A083388 A083389 A083390 * A083392 A083393 A083394

Keyword

nonn

Author

David Terr, Jun 11 2003

Extensions

Name clarified by Sean A. Irvine, Jan 21 2026

Status

approved