A083556 - OEIS

%I #3 Mar 31 2012 20:35:51

%S 3,9,15,105,105,105,105,105,165,165,75075,75075,75075,75075,75075,

%T 75075,855855,855855,5583435,5583435,5583435,18625035,18625035,

%U 18625035,18625035,18625035,27183585,27183585,27183585,27183585,27183585

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

%H Author?, <a href="http://home.btclick.com/rwsmith/pp/payam3.htm">Title?</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PayamNumber.html">Payam Number</a>

%e 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 Cf. A080076.

%Y Cf. A083391.

%K hard,nonn

%O 2,1

%A _David Terr_, Jun 10 2003