A102926 Smallest prime factor in product of previous terms +1 or -1.

2, 3, 5, 29, 11, 7, 13, 37, 17, 79, 23, 4129, 193, 2593, 101, 19, 39163, 577, 26431, 131, 308798542881428667318174028327605372989, 103, 163, 179, 293, 127, 6287, 683437, 31, 89, 13590243019242466336587034391, 113, 2207, 59, 109, 223, 2351

Offset

1,1

Comments

A variant of the Euclid-Mullin construction.

This sequence is listed on the OEIS wiki page "OEIS sequences needing factors" and on the corresponding thread on mersenneforum.org. - M. F. Hasler, Mar 21 2013

Links

Donovan Johnson, Table of n, a(n) for n = 1..111

Formula

a(n) = least prime factor of b(n)^2-1, where b(n) = product a(k), 0<k<n, = A102927.

Example

a(5)=11 because 2*3*5*29=870, 869=11*79, 871=13*67.
a(31) = 13590243019242466336587034391 because this is the least prime factor of A102927(30)+1. The least prime factor of A102927(30)-1 is 44989026625856465412069667987. Remarkably, both are 29-digit numbers. - David Wasserman, Apr 15 2008

Mathematica

spf[{p_, a_}]:=With[{f=FactorInteger[p^2-1][[1, 1]]}, {p*f, f}]; NestList[ spf, {2, 2}, 36][[All, 2]] (* Harvey P. Dale, May 05 2018 *)

Crossrefs

Cf. A000945, A000946, A005265, A102927.

Sequence in context: A178376 A041585 A042935 * A084598 A215307 A215103

Adjacent sequences: A102923 A102924 A102925 * A102927 A102928 A102929

Keyword

nonn

Author

Marc LeBrun, Jan 19 2005

Extensions

More terms from Don Reble, Jan 23 2005, corrected Sep 26 2006

Further terms from David Wasserman, Apr 15 2008

Status

approved