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 A144932 Integers n such that n^2 + k is a Mersenne number 2^m - 1 for some k < n and m odd. 3
 1, 11, 45, 181, 362, 724, 1448, 2896, 11585, 23170, 741455, 1482910, 11863283, 23726566, 189812531, 379625062, 97184015999, 194368031998, 3109888511975, 99516432383215, 199032864766430, 1592262918131443, 3184525836262886 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Subset of A017910. The corresponding Mersenne number exponents are given by A144931. Contribution from Gil Broussard, Sep 12 2009: (Start) It appears that a(n) are the only numbers with this property: the binary expansion of a(n) is identical to the first ceil(log base 2 of 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 .000101000101110100010111010... Table of a(2) to a(11): 11 1011 -> .0001010001011101000101110100010111010001011... 45 101101 -> .00000100000101101100000101101100000101101... 181 10110101 -> .000000000001001111001101000101010011011... 362 101101010 -> .00000000000100111100110100010101001101... 724 1011010100 -> .0000000000010011110011010001010100110... 1448 10110101000 -> .000000000001001111001101000101010011... 2896 101101010000 -> .00000000000100111100110100010101001... 11585 10110101000001 -> .000000000000001111001100110100100... 23170 101101010000010 -> .00000000000000111100110011010010... 741455 10110101000001001111 -> .000000000000000000001100110... (End) LINKS PROG (PARI) forstep(m=1, 10^6, 2, n=sqrtint(2^m-1); if(2^m-1-n^2

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Last modified November 21 01:23 EST 2019. Contains 329348 sequences. (Running on oeis4.)