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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.
18
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
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
Will Edgington, Factored Mersenne Numbers [from Internet Archive Wayback Machine]
PROG
(PARI) A112927(n, f=factor(2^n-1)[, 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^n-1 is too slow. You may try factor(2^n-1, 0)[, 1]. - M. F. Hasler, Feb 21 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Aug 25 2008
STATUS
approved