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 A217993 Smallest k such that k^(2^n) + 1 and (k+2)^(2^n) + 1 are both prime. 1
 2, 2, 2, 2, 74, 112, 2162, 63738, 13220, 54808, 3656570, 6992032, 125440, 103859114, 56414914, 87888966 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified March 20 05:51 EDT 2023. Contains 361359 sequences. (Running on oeis4.)