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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 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.

CROSSREFS

Cf. A083556.

Cf. A080076.

Sequence in context: A059495 A174325 A290366 * A165636 A142469 A009809

Adjacent sequences:  A083388 A083389 A083390 * A083392 A083393 A083394

KEYWORD

nonn

AUTHOR

David Terr, Jun 11 2003

STATUS

approved

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Last modified October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)