A144932 Integers n such that n^2 + k is a Mersenne number 2^m - 1 for some k < n and m odd.

1, 11, 45, 181, 362, 724, 1448, 2896, 11585, 23170, 741455, 1482910, 11863283, 23726566, 189812531, 379625062, 97184015999, 194368031998, 3109888511975, 99516432383215, 199032864766430, 1592262918131443, 3184525836262886

Offset

1,2

Comments

Subset of A017910.

The corresponding Mersenne number exponents are given by A144931.

From Gil Broussard, Sep 12 2009: (Start)

It appears that the terms of this sequence are the only numbers with this property: the binary expansion of a(n) is identical to the first ceiling(log_2(a(n))) nonzero digits of the binary expansion of 1/a(n). In other words, if the binary expansion of a(n) is 6 digits, then the first 6 nonzero digits of the binary expansion of 1/a(n) is identical for some a(n).

For example:

a(2)=11=binary 1011 which is 4 digits long and equivalent to the first 4 digits of its binary reciprocal (after the initial zeros):

1/a(2) = binary .000[1011]101000101110100010111010...

Table of a(2) to a(11):

11 1011 -> .000[1011]1010001011101000101110100010111010001011...

45 101101 -> .00000[101101]100000101101100000101101100000101101...

181 10110101 -> .0000000[10110101]00001001111001101000101010011011...

362 101101010 -> .00000000[101101010]000100111100110100010101001101...

724 1011010100 -> .000000000[1011010100]0010011110011010001010100110...

1448 10110101000 -> .0000000000[10110101000]01001111001101000101010011...

2896 101101010000 -> .00000000000[101101010000]100111100110100010101001...

11585 10110101000001 -> .0000000000000[10110101000001]01111001100110100100...

23170 101101010000010 -> .00000000000000[101101010000010]111100110011010010...

741455 10110101000001001111 -> .0000000000000000000[10110101000001001111]01100110...

(End)

Links

Table of n, a(n) for n=1..23.

Prog

(PARI) forstep(m=1, 10^6, 2, n=sqrtint(2^m-1); if(2^m-1-n^2<n, print1(n, ", ")))

Crossrefs

Cf. A000225, A017910, A144931.

Sequence in context: A051740 A370534 A263227 * A072262 A231224 A231438

Adjacent sequences: A144929 A144930 A144931 * A144933 A144934 A144935

Keyword

nonn

Author

Reikku Kulon, Sep 25 2008

Extensions

Edited by Max Alekseyev, Oct 12 2009

Edited by Charles R Greathouse IV, Mar 23 2010

Status

approved