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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
OFFSET
2,1
COMMENTS
Payam numbers yield many primes of the form k*2^n+1 (Proth primes) and k*2^n-1.
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: A372423 A174325 A290366 * A165636 A142469 A009809
KEYWORD
nonn
AUTHOR
David Terr, Jun 11 2003
STATUS
approved