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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. 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 (list; graph; refs; listen; history; text; internal format)
 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^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 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

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Last modified May 15 04:03 EDT 2021. Contains 343909 sequences. (Running on oeis4.)