id:A144932 - OEIS Search Results

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

+0
4

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; listen)

	OFFSET	`1,2`
	COMMENT	`Subset of A017910.` `The corresponding Mersenne number exponents are given by A144931.` `Contribution from Gil Broussard (gilbroussard(AT)bellsouth.net), 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 zeroes):` `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)`
	PROGRAM	`(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: A154106 A057813 A051740 this_sequence A072262 A110114 A116193` `Adjacent sequences: A144929 A144930 A144931 this_sequence A144933 A144934 A144935`
	KEYWORD	`nonn`
	AUTHOR	`Reikku Kulon (reikku(AT)gmail.com), Sep 25 2008`
	EXTENSIONS	`Edited by Max Alekseyev, Oct 12 2009`

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Last modified November 30 13:13 EST 2009. Contains 167758 sequences.

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