A014741 Numbers k such that k divides 2^(k+1) - 2.

1, 2, 6, 18, 42, 54, 126, 162, 294, 342, 378, 486, 882, 1026, 1134, 1314, 1458, 1806, 2058, 2394, 2646, 3078, 3402, 3942, 4374, 5334, 5418, 6174, 6498, 7182, 7938, 9198, 9234, 10206, 11826, 12642, 13122, 14154, 14406, 16002, 16254

Offset: 1

Author

N. J. A. Sloane, Olivier Gérard

Keywords

• nonn

Comments

Also, numbers k such that k divides Eulerian number A000295(k+1) = 2^(k+1) - k - 2.

Also, numbers k such that k divides A086787(k) = Sum_{i=1..k} Sum_{j=1..k} i^j.

All terms greater than 1 are even; for a proof, see comment in A036236. - Max Alekseyev, Feb 03 2012

If k>1 is a term, then 3*k is also a term. - Alexander Adamchuk, Nov 03 2006

Prime numbers of the form a(m)+1 are given by A069051. - Max Alekseyev, Nov 14 2012

The number 2^m - 2 is a term of this sequence if and only if m - 1 is a term. - Thomas Ordowski, Jul 01 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000295, A086787, A015919, A006517, A330382.

Programs

Mathematica

Join[{1,2},Select[Range[17000],PowerMod[2,#+1,#]==2&]] (* Harvey P. Dale, Feb 11 2015 *)

PARI

is(n)=Mod(2,n)^(n+1)==2 \\ Charles R Greathouse IV, Nov 03 2016

Formula

For n > 1, a(n) = 2*A014945(n-1). - Max Alekseyev, Nov 14 2012