

A102926


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


2



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



OFFSET

1,1


COMMENTS

A variant of the EuclidMullin 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)^21, 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 29digit numbers.  David Wasserman, Apr 15 2008


MATHEMATICA

spf[{p_, a_}]:=With[{f=FactorInteger[p^21][[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



