A246648 Numbers k such that 2*k + 1 divides 2^(k+1) - 1.

0, 1, 7, 127, 227, 647, 1351, 1907, 3239, 4607, 5219, 5975, 11447, 13159, 13919, 21527, 22049, 23759, 23939, 24839, 30959, 31283, 31583, 31967, 32767, 37223, 46091, 46511, 47267, 60479, 65663, 66527, 78539, 78599, 81727, 82799, 84311, 98405, 102671, 103967

Offset

1,3

Comments

These are the numbers k such that mean of the k-th row of the triangle at A027926 is an integer.

Numbers k such that 2*k + 1 divides 2^k + k. - Thomas Ordowski, Jun 04 2024

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

The sum of the numbers row 7 of the triangular array at A027926 is 2^8 - 1 = 255, and the number of numbers in row 7 is 15, and 255/15 = 17; thus 7 is in this sequence, and 17 is in A246649.

Maple

filter:= k -> 2 &^ (k+1) - 1 mod (2*k+1) = 0:
select(filter, [$0..2*10^5]); # Robert Israel, Jan 10 2020

Mathematica

z = 140000; u = Select[Range[0, z], IntegerQ[(2^(# + 1) - 1)/(2 # + 1)] &]   (* A246648 *)
v = Table[(2^(u[[k]] + 1) - 1)/(2 u[[k]] + 1), {k, 1, 6}] (* A246649 *)
Join[{0}, Select[Range[105000], PowerMod[2, #+1, 2#+1]==1&]] (* Harvey P. Dale, Sep 11 2025 *)

Crossrefs

Cf. A246637, A246649.

Sequence in context: A202798 A204248 A084940 * A308378 A139987 A061744

Adjacent sequences: A246645 A246646 A246647 * A246649 A246650 A246651

Keyword

nonn,easy

Author

Clark Kimberling, Sep 01 2014

Extensions

Edited and offset changed by Robert Israel, Jan 10 2020

Status

approved