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

0,1

Comments

a(15)=87888966 but a(14) is unknown. - Jeppe Stig Nielsen, Mar 17 2018

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

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = A118539(n)-1. - Jeppe Stig Nielsen, Feb 27 2016

Example

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.

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:

Crossrefs

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

Sequence in context: A225057 A084954 A226281 * A049300 A339017 A084957

Adjacent sequences: A217990 A217991 A217992 * A217994 A217995 A217996

Keyword

nonn,hard,more

Author

Michel Lagneau, Oct 17 2012

Extensions

a(13) from Jeppe Stig Nielsen, Mar 17 2018

a(14) and a(15) from Jeppe Stig Nielsen, May 02 2018

Status

approved