A263686 -id:A263686 - cp's OEIS frontend

A309130 Smallest prime factor of A077586(n).

7, 127, 2147483647, 170141183460469231731687303715884105727, 47, 338193759479, 231733529, 62914441, 2351, 1399, 295257526626031, 18287, 106937, 863, 4703, 138863, 22590223644617

Offset: 1

Richard N. Smith, Jul 13 2019

A263686 is a subsequence.
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.
a(18) = A263686(9) is greater than 1.56*10^17*(2^61-1), see link.
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.
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).
Conjecture: All terms are in A122094 (all terms in A263686 are in A122094).
For examples related to that conjecture, see A322568. - Jeppe Stig Nielsen, Aug 29 2019
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

Double Mersennes Prime Search, History.
Eric Weisstein's World of Mathematics, Double Mersenne Number.

Cf. A077586, A263686, A001348, A049479.

A309130(n)=A020639(2^(2^prime(n)-1)-1) \\ For efficiency, use addprimes([large terms of this sequence]). - M. F. Hasler, Mar 01 2025

a(n) = A020639(A077586(n)).

a(n) = A049479(A001348(n)). - M. F. Hasler, Mar 01 2025

A276641 Number of digits in 2^A000668(n)-1.

Original entry on oeis.org

1, 3, 10, 39, 2466, 39457, 157827, 646456993, 694127911065419642, 186328542329173367306815834, 48844909400338823199277929902126, 51217599719369681875006054625051616350

Offset: 1

Felix Fröhlich, Sep 22 2016

The sequence is a subsequence of A227683.

Ivan Panchenko, Table of n, a(n) for n = 1..18
MathWorld, Double Mersenne Number.
Wikipedia, Double Mersenne number.

Cf. A227683, A263686.

next_a000668(n) = my(expo=nextprime(ceil(log(n+1)/log(2)))); while(!ispseudoprime(2^expo-1), expo=nextprime(expo+1)); 2^expo-1
terms(n) = my(p=3, i=0); while(i < n, print1(#Str(2^p-1), ", "); i++; p=next_a000668(p+1))
terms(7) \\ print initial seven terms

a(n) = A055642(A000225(A000668(n))).

a(8)-a(12) from Ivan Panchenko, Apr 11 2018

A277634 a(n) = 2^A000668(n) - 1.

Original entry on oeis.org

7, 127, 2147483647, 170141183460469231731687303715884105727

Offset: 1

Felix Fröhlich, Oct 24 2016

The terms of this sequence are sometimes called "Double Mersenne numbers" (cf. A263686).
Agrees with A077586 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.
a(5) is too large to include in data section (see A276641).
a(n) = A263686(n) iff a(n) is prime, which is the case iff A000668(n) is in A103901.
Agrees with A263686 at least in the first four terms. - Omar E. Pol, Oct 24 2016

Cf. A000043, A000225, A000668, A077586, A103901, A263686, A276641.

forprime(p=1, 11, if(ispseudoprime(2^p-1), print1(2^(2^p-1)-1, ", ")))

a(n) = A000225(A000668(n)).

cp's OEIS Frontend

A309130 Smallest prime factor of A077586(n).

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A276641 Number of digits in 2^A000668(n)-1.

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A277634 a(n) = 2^A000668(n) - 1.

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