

A034881


a(1) = 1; for n>1, a(n) = smallest integer > a(n1) such that a(n)*a(i)+1 is prime for all 1 <= i <= n1.


5



1, 2, 6, 18, 30, 270, 606, 123120, 888456, 23070450, 238550160, 8282903640, 72789145650, 15681266370000, 18216437241240
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OFFSET

1,2


COMMENTS

a(16) > 2*10^16.
a(n) exists for every n if Dickson's conjecture is true.  Charles R Greathouse IV, Nov 30 2012


LINKS

Table of n, a(n) for n=1..15.
Bill Taylor et al., Sets producing primes, sci.math (2003)


EXAMPLE

After a(1)=1, a(2)=2, a(3)=6, we want m, the smallest number >6 such that m+1, 2m+1 and 6m+1 are all prime: this is m = 18 = a(4).


MATHEMATICA

f[s_List] := Block[{k = s[[1]] + 1, m = s}, While[ Union@ PrimeQ[k*m + 1] != {True}, k++]; Append[s, k]]; Nest[f, {1}, 10] (* Robert G. Wilson v, Dec 02 2012 *)


CROSSREFS

Cf. A219761, A093483.
Sequence in context: A288815 A277200 A277324 * A146345 A328633 A064842
Adjacent sequences: A034878 A034879 A034880 * A034882 A034883 A034884


KEYWORD

nonn


AUTHOR

Erich Friedman


EXTENSIONS

a(9)a(13) found by Phil Carmody.
a(14)a(15) from Don Reble, Oct 15 2012
Edited by N. J. A. Sloane, Dec 01 2012


STATUS

approved



