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A217993 Smallest k such that k^(2^n) + 1 and (k+2)^(2^n) + 1 are both prime. 1

%I #18 May 03 2018 03:04:14

%S 2,2,2,2,74,112,2162,63738,13220,54808,3656570,6992032,125440,

%T 103859114,56414914,87888966

%N Smallest k such that k^(2^n) + 1 and (k+2)^(2^n) + 1 are both prime.

%C a(15)=87888966 but a(14) is unknown. - _Jeppe Stig Nielsen_, Mar 17 2018

%C The prime pair related to a(14) was found four days ago, and today double checking has proved that they are indeed the first occurrence for n=14. - _Jeppe Stig Nielsen_, May 02 2018

%F a(n) = A118539(n)-1. - _Jeppe Stig Nielsen_, Feb 27 2016

%e a(0) = 2 because 2^1+1 = 3 and 4^1+1 = 5 are prime;

%e a(1) = 2 because 2^2+1 = 5 and 4^2+1 = 17 are prime;

%e a(2) = 2 because 2^4+1 = 17 and 4^4+1 = 257 are prime;

%e a(3) = 2 because 2^8+1 = 257 and 4^8+1 = 65537 are prime.

%p 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:

%Y Cf. A006313, A006314, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A118539.

%K nonn,hard,more

%O 0,1

%A _Michel Lagneau_, Oct 17 2012

%E a(13) from _Jeppe Stig Nielsen_, Mar 17 2018

%E a(14) and a(15) from _Jeppe Stig Nielsen_, May 02 2018

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Last modified March 29 02:13 EDT 2024. Contains 371264 sequences. (Running on oeis4.)