

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.


10



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
Bang's theorem (special case of Zsigmondy's theorem, see links): a(n)>1 for all n>6.  Jeppe Stig Nielsen, Aug 31 2020


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]
Wikipedia, Zsigmondy's theorem


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: A112071 A231609 A046561 * A097406 A064078 A292015
Adjacent sequences: A112924 A112925 A112926 * A112928 A112929 A112930


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Aug 25 2008


STATUS

approved



