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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. 1
3, 9, 15, 105, 105, 105, 105, 105, 165, 165, 75075, 75075, 75075, 75075, 75075, 75075, 855855, 855855, 5583435, 5583435, 5583435, 18625035, 18625035, 18625035, 18625035, 18625035, 27183585, 27183585, 27183585, 27183585, 27183585 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
Payam numbers are good candidates for looking for Proth primes, i.e. primes of the form k*2^n+1
LINKS
Author?, Title?
Eric Weisstein's World of Mathematics, Payam Number
EXAMPLE
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.
CROSSREFS
Cf. A080076.
Cf. A083391.
Sequence in context: A348199 A242438 A355716 * A015664 A272621 A134137
KEYWORD
hard,nonn
AUTHOR
David Terr, Jun 10 2003
STATUS
approved

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Last modified August 6 03:16 EDT 2024. Contains 374957 sequences. (Running on oeis4.)