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A057325
First member of a prime quadruple in a p^2+p-1 progression.
3
3, 11, 53, 1693, 2663, 4423, 16831, 17609, 36229, 49801, 94961, 121493, 150869, 176303, 183761, 188011, 210901, 213833, 218579, 272903, 300301, 329671, 439511, 444791, 453023, 469613, 518813, 531911, 546071, 559703, 570719, 614279, 705781
OFFSET
1,1
COMMENTS
I found only one prime 5-tuple so far: (3,11,131,17291,298995971).
Subsequence of A057324. - Pierre CAMI, Sep 13 2013
EXAMPLE
3 -> 3^2+3-1 = 11 -> 11^2+11-1 = 131 -> 131^2+131-1 = 17291 hence the quadruple (3,11,131,17291).
MATHEMATICA
okQ[n_] := And@@PrimeQ/@NestList[#^2 + # - 1 &, n, 3];
Select[ Prime[ Range[ 60000]], okQ] (* Harvey P. Dale, Jan 05 2011 *)
PROG
(PARI) is(n)=for(k=1, 4, if(!isprime(n), return(0)); n=n^2+n-1); 1 \\ Charles R Greathouse IV, Sep 13 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Patrick De Geest, Aug 15 2000
EXTENSIONS
Offset changed by Andrew Howroyd, Aug 14 2024
STATUS
approved