A083391 - OEIS

%I #4 Feb 16 2025 08:32:49

%S 3,3,45,45,45,45,45,45,2145,2805,92235,92235,92235,92235,92235,92235,

%T 529815,529815,529815,529815,529815,529815,529815,529815,1426425,

%U 1426425,247016055,247016055,247016055,247016055

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

%H Robert Smith, <a href="http://home.btclick.com/rwsmith/pp/payam3.htm">A coordinated search for primes in the Payam number series</a>.

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

%e 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

%e equal to 4.

%Y Cf. A083556.

%Y Cf. A080076.

%K nonn

%O 2,1

%A _David Terr_, Jun 11 2003