A289982 Lesser member p of twin primes in A054723 (Prime exponents of composite Mersenne numbers).

41, 71, 101, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607, 1619, 1667, 1697, 1721, 1787, 1871, 1877

Offset

1,1

Comments

2^p-1 is composite. p is the lesser of twin primes in A001359 and a prime exponent of a Mersenne number in A054723.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

p=41 is a member because 41 is a lesser of twin prime and 2^41 - 1 = 13367*164511353 is composite.
Similarly, p=227 is a member because 227 is a lesser of twin prime and 2^227 - 1 is composite.

Mathematica

Function[s, Flatten@ Map[s[[#, 1]] &, Position[Most@ s, d_ /; Quiet@ Differences@ d == {2}, {1}]]]@ Partition[#, 2, 1] &@ Select[Prime@ Range@ 360, ! PrimeQ[2^# - 1] &] (* Michael De Vlieger, Jul 17 2017 *)
Select[Partition[Module[{nn=20, mp}, mp=MersennePrimeExponent[Range[nn]]; Complement[Prime[Range[PrimePi[Last[mp]]]], mp]], 2, 1], #[[2]]-#[[1]]==2 && AllTrue[#, PrimeQ]&][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 10 2019 *)

Prog

(GAP)
P1:=Difference(Filtered([1..100000], IsPrime), [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243]);;
P2:=List([1..Length(P1)-1], i->[P1[i], P1[i+1]]);;
P3:=List(Positions(List(P2, i->i[2]-i[1]), 2), i->P2[i][1]);
(PARI) isok(n) = isprime(n) && isprime(n+2) && !isprime(2^n-1) && !isprime(2^(n+2)-1); \\ Michel Marcus, Jul 19 2017

Crossrefs

Subsequence of A054723.

Cf. A001097, A001359, A006512, A077800.

Sequence in context: A140374 A334765 A269807 * A054806 A057540 A362592

Adjacent sequences: A289979 A289980 A289981 * A289983 A289984 A289985

Keyword

nonn

Author

Muniru A Asiru, Jul 17 2017

Status

approved