A119691 -id:A119691 - cp's OEIS frontend

A132143 Prime numbers P such that (P^k-2) is not divisible by 35(=A119691(1)) for any value of k.

3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 47, 59, 61, 71, 73, 79, 83, 89, 97, 101, 103, 109, 113, 127, 131, 139, 149, 151, 157, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 239, 241, 251, 257, 269, 271, 281, 283, 293, 307, 311, 313, 331, 337, 349, 353

Offset: 1

A.K. Devaraj, Aug 12 2007

Primes not congruent to 2, 18, 23, or 32 (mod 35). - Robert Israel, Jan 14 2019

A. K. Devaraj, "Euler's Generalization of Fermat's Theorem-A Further Generalization", in ISSN #1550-3747, Proceedings of Hawaii Intl Conference on Statistics, Mathematics & Related Fields, 2004.

Robert Israel, Table of n, a(n) for n = 1..10000

G:= sort(convert(map(proc(t) if t::even then t+35 else t fi end proc, {$0..34} minus {2,18,23,32}),list)):
select(isprime, [seq(seq(70*i+j,j=G),i=0..10)]); # Robert Israel, Jan 14 2019

forprime(p=1, 353, if(#setintersect([p%35], [2, 18, 23, 32])==0, print1(p, ", "))) \\ Felix Fröhlich, Jan 14 2019

Terms beyond 41 from R. J. Mathar, Mar 01 2010

A131960 a(n) = A000043(n) * A000668(n).

Original entry on oeis.org

6, 21, 155, 889, 106483, 2228207, 9961453, 66571993057, 140656423562035331011, 55088331748199422233011027879, 17361742620725829882898847100829589, 21607930299479592429924287571917281427329

Offset: 1

A.K. Devaraj, Aug 02 2007, Aug 06 2007

Note that a(3) = 155 and a(4) = 889 also belong to A119691.
Old name was: Composite numbers such that the first factor is the relevant exponent of Mersenne prime (the second factor).
a(n) is the smallest k > 0 such that A000668(n)^2 divides 2^k-1. Then lpf(2^k-1) = A000668(n), where lpf(m) = A020639(m). - Thomas Ordowski, Feb 03 2019

Amiram Eldar, Table of n, a(n) for n = 1..18

Cf. A000043, A000668, A002326, A020639, A119691.

Map[# * (2^#-1) &, MersennePrimeExponent[Range[12]]] (* Amiram Eldar, Oct 21 2024 *)

expm = [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127]; vector(#expm, i, expm[i]*(2^expm[i]-1)) \\ where expm comes from A000043; Michel Marcus, Feb 07 2019

a(n) = A000043(n)*A000668(n). - R. J. Mathar, Oct 18 2007

a(n) = A002326((A000668(n)^2 - 1)/2). - Thomas Ordowski, Feb 03 2019

Terms corrected, edited, and new name by Michel Marcus, Apr 30 2013

a(12) from Michel Marcus, Feb 07 2019

cp's OEIS Frontend

A132143 Prime numbers P such that (P^k-2) is not divisible by 35(=A119691(1)) for any value of k.

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