%I #43 Jan 25 2024 14:31:10
%S 7,127,2147483647,170141183460469231731687303715884105727,47,
%T 338193759479,231733529,62914441,2351,1399,295257526626031,18287,
%U 106937,863,4703,138863,22590223644617
%N Smallest prime factor of A077586(n).
%C A263686 is a subsequence.
%C Agrees with A263686 in the first four terms, but then the two sequences differ for the first time at n = 5, because prime(5) = 11 is not in A000043.
%C a(18) = A263686(9) is greater than 1.56*10^17*(2^61-1), see link.
%C a(n) = A077586(n) iff A077586(n) is prime, A077586(n) is prime for 1<=n<=4, but composite for 5<=n<=17. The status of A077586(18) = 2^(2^61-1)-1 is unknown. It is conjectured that A077586(n) is composite for all n>=5.
%C a(20) = 456959, a(21) = 18384329, a(22) = 198839, a(23) = 2349023, a(24) = A263686(10) is greater than 1.25*10^16*(2^89-1).
%C Conjecture: All terms are in A122094 (all terms in A263686 are in A122094).
%C For examples related to that conjecture, see A322568. - _Jeppe Stig Nielsen_, Aug 29 2019
%C a(30) = 46559, a(32) = 23671, a(36) = 7151489, a(39) = 4698047, a(41) = 719, a(43) = 1440847, a(45) = 179689, a(47) = 11759383, a(48) = 23602441, a(50) = 9024439, a(51) = 28875361, a(52) = 6301423, a(54) = 2493983, a(56) = 33518137, a(59) = 6727783, a(66) = 95111, a(72) = 1439, a(73) = 99833, a(78) = 38119, a(81) = 26849, a(83) = 8258911, a(86) = 16173559, a(89) = 625343, a(93) = 9743. - _Chai Wah Wu_, Oct 16 2019
%H Double Mersennes Prime Search, <a href="http://www.doublemersennes.org/history.php">History</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DoubleMersenneNumber.html">Double Mersenne Number</a>.
%F a(n) = A020639(A077586(n)).
%Y Cf. A077586, A263686.
%K nonn,hard,more
%O 1,1
%A _Richard N. Smith_, Jul 13 2019