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

%I #12 Jan 11 2020 00:48:25

%S 0,1,7,127,227,647,1351,1907,3239,4607,5219,5975,11447,13159,13919,

%T 21527,22049,23759,23939,24839,30959,31283,31583,31967,32767,37223,

%U 46091,46511,47267,60479,65663,66527,78539,78599,81727,82799,84311,98405,102671,103967

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

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

%H Robert Israel, <a href="/A246648/b246648.txt">Table of n, a(n) for n = 1..2000</a>

%e 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.

%p filter:= k -> 2 &^ (k+1) - 1 mod (2*k+1) = 0:

%p select(filter, [$0..2*10^5]); # _Robert Israel_, Jan 10 2020

%t z = 140000; u = Select[Range[0, z], IntegerQ[(2^(# + 1) - 1)/(2 # + 1)] &] (* A246648 *)

%t v = Table[(2^(u[[k]] + 1) - 1)/(2 u[[k]] + 1), {k, 1, 6}] (* A246649 *)

%Y Cf. A246637, A246649.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, Sep 01 2014

%E Edited and offset changed by _Robert Israel_, Jan 10 2020

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)