

A112927


a(n) is the least prime such that the multiplicative order of 2 mod a(n) equals n, or a(n)=1 if no such prime exists.


7



1, 3, 7, 5, 31, 1, 127, 17, 73, 11, 23, 13, 8191, 43, 151, 257, 131071, 19, 524287, 41, 337, 683, 47, 241, 601, 2731, 262657, 29, 233, 331, 2147483647, 65537, 599479, 43691, 71, 37, 223, 174763, 79, 61681, 13367, 5419, 431, 397, 631, 2796203, 2351, 97, 4432676798593, 251, 103, 53, 6361, 87211
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OFFSET

1,2


COMMENTS

If a(n) differs from 1, then a(n) is the minimal prime divisor of A064078(n);
a(n)=n+1 iff n+1 is prime from A001122; a(n)=2n+1 iff 2n+1 is prime from A115591.
If a(n) > 1 then a(n) is the index where n occurs first in A014664.  M. F. Hasler, Feb 21 2016


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..606 (shortened by N. J. A. Sloane, Jan 18 2019)
Dario Alejandro Alpern, Factorization using the Elliptic Curve Method
Will Edgington, Factored Mersenne Numbers [from Internet Archive Wayback Machine]


PROG

(PARI) A112927(n, f=factor(2^n1)[, 1])=!for(i=1, #f, znorder(Mod(2, f[i]))==n&&return(f[i])) \\ Use the optional 2nd arg to give a list of pseudoprimes to try when factoring of 2^n1 is too slow. You may try factor(2^n1, 0)[, 1].  M. F. Hasler, Feb 21 2016


CROSSREFS

Cf. A002326, A064078, A001122, A115591.
Sequence in context: A231609 A046561 A097406 * A064078 A292015 A186522
Adjacent sequences: A112924 A112925 A112926 * A112928 A112929 A112930


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Aug 25 2008


STATUS

approved



