

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
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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



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



KEYWORD

nonn


AUTHOR



EXTENSIONS

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


STATUS

approved



