A217993 Smallest k such that k^(2^n) + 1 and (k+2)^(2^n) + 1 are both prime.
2, 2, 2, 2, 74, 112, 2162, 63738, 13220, 54808, 3656570, 6992032, 125440, 103859114, 56414914, 87888966
Offset: 0
Examples
a(0) = 2 because 2^1+1 = 3 and 4^1+1 = 5 are prime; a(1) = 2 because 2^2+1 = 5 and 4^2+1 = 17 are prime; a(2) = 2 because 2^4+1 = 17 and 4^4+1 = 257 are prime; a(3) = 2 because 2^8+1 = 257 and 4^8+1 = 65537 are prime.
Crossrefs
Programs
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Maple
for n from 0 to 5 do:ii:=0:for k from 2 by 2 to 10000 while(ii=0) do:if type(k^(2^n)+1,prime)=true and type((k+2)^(2^n)+1,prime)=true then ii:=1: printf ( "%d %d \n",n,k):else fi:od:od:
Formula
a(n) = A118539(n)-1. - Jeppe Stig Nielsen, Feb 27 2016
Extensions
a(13) from Jeppe Stig Nielsen, Mar 17 2018
a(14) and a(15) from Jeppe Stig Nielsen, May 02 2018
Comments