A083391 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, 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

Author

David Terr, Jun 11 2003

Keywords

• nonn

Comments

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

Examples

			E_{-}(4) = 45 because 45 is the smallest odd integer k such that for every nonnegative integer n, k*2^n-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.
		

Links

• Robert Smith, A coordinated search for primes in the Payam number series.
• Eric Weisstein's World of Mathematics, Payam Number

Crossrefs

Cf. A083556.

Cf. A080076.