cp's OEIS Frontend

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.

%I A083556 #4 Feb 16 2025 08:32:49
%S A083556 3,9,15,105,105,105,105,105,165,165,75075,75075,75075,75075,75075,
%T A083556 75075,855855,855855,5583435,5583435,5583435,18625035,18625035,
%U A083556 18625035,18625035,18625035,27183585,27183585,27183585,27183585,27183585
%N 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.
%C A083556 Payam numbers are good candidates for looking for Proth primes, i.e. primes of the form k*2^n+1
%H A083556 Author?, <a href="http://home.btclick.com/rwsmith/pp/payam3.htm">Title?</a>
%H A083556 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PayamNumber.html">Payam Number</a>
%e A083556 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.
%Y A083556 Cf. A080076.
%Y A083556 Cf. A083391.
%K A083556 hard,nonn
%O A083556 2,1
%A A083556 _David Terr_, Jun 10 2003