

A108403


Numbers n such that n^26 and n^2+6 are both prime.


1



5, 25, 65, 145, 355, 605, 985, 1075, 1295, 1465, 1565, 1675, 1915, 2345, 2425, 2585, 2755, 3005, 3155, 3785, 4595, 4625, 4975, 5225, 5465, 5665, 5905, 5915, 6115, 6295, 6305, 6415, 6485, 7235, 7775, 8185, 9065, 9275, 9415, 9755, 9835, 10145, 10195
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OFFSET

1,1


COMMENTS

All members of the sequence are divisible by 5 as if n is 1 or 4 mod 5 then n^26 is divisible by 5 and if n is 2 or 3 mod 5 then n^2+6 is divisible by 5.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


EXAMPLE

a(2)=25 since 25^2  6 = 619 and 25^2 + 6 = 631 are both prime.


MATHEMATICA

pQ[n_]:=Module[{n2=n^2}, And@@PrimeQ[{n26, n2+6}]]; Select[5Range[2100], pQ] (* Harvey P. Dale, Nov 06 2011 *)


PROG

(MAGMA) [n: n in [2..100000]  IsPrime(n^26) and IsPrime(n^2+6)] // Vincenzo Librandi, Nov 13 2010


CROSSREFS

Cf. A087681 (with n instead of n^2), A108701 (with 2 instead of 6).
Sequence in context: A323187 A179131 A054994 * A007058 A071383 A088959
Adjacent sequences: A108400 A108401 A108402 * A108404 A108405 A108406


KEYWORD

nonn


AUTHOR

John L. Drost, Jul 04 2005


STATUS

approved



