This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309130 #46 Mar 02 2025 22:57:27 %S A309130 7,127,2147483647,170141183460469231731687303715884105727,47, %T A309130 338193759479,231733529,62914441,2351,1399,295257526626031,18287, %U A309130 106937,863,4703,138863,22590223644617 %N A309130 Smallest prime factor of A077586(n). %C A309130 A263686 is a subsequence. %C A309130 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 A309130 a(18) = A263686(9) is greater than 1.56*10^17*(2^61-1), see link. %C A309130 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 A309130 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 A309130 Conjecture: All terms are in A122094 (all terms in A263686 are in A122094). %C A309130 For examples related to that conjecture, see A322568. - _Jeppe Stig Nielsen_, Aug 29 2019 %C A309130 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 A309130 Double Mersennes Prime Search, <a href="http://www.doublemersennes.org/history.php">History</a>. %H A309130 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DoubleMersenneNumber.html">Double Mersenne Number</a>. %F A309130 a(n) = A020639(A077586(n)). %F A309130 a(n) = A049479(A001348(n)). - _M. F. Hasler_, Mar 01 2025 %o A309130 (PARI) A309130(n)=A020639(2^(2^prime(n)-1)-1) \\ For efficiency, use addprimes([large terms of this sequence]). - _M. F. Hasler_, Mar 01 2025 %Y A309130 Cf. A077586, A263686, A001348, A049479. %K A309130 nonn,hard,more %O A309130 1,1 %A A309130 _Richard N. Smith_, Jul 13 2019