A260477 Numbers n where n^2 is an anagram of (n+1)^2 in base 2.

9, 17, 33, 49, 50, 65, 73, 77, 85, 86, 97, 106, 129, 137, 149, 157, 161, 165, 178, 186, 193, 201, 212, 213, 225, 226, 257, 265, 273, 279, 281, 285, 300, 305, 307, 310, 317, 321, 325, 332, 334, 345, 355, 365, 366, 378, 385, 393, 394, 413, 426, 427, 449, 469

Offset: 1

Author

Dhilan Lahoti, Aug 28 2015

Keywords

• base
• easy
• nonn

Comments

Base 2 equivalent of A072841.

It appears that one of these numbers has a 1/n chance of being divisible by an odd number n, but a smaller than 1/n chance if n is even.

Examples

			17 is a term of the sequence because its square base 2 (100100001) and 18's square base 2 (101000100) are anagrams.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Mathematica

For[i = 1, i <= 10000, i++,
If[Sort[IntegerDigits[i^2, 2]] == Sort[IntegerDigits[(i + 1)^2, 2]],
  Print[i]]]

PARI

is(n)=hammingweight(n^2)==hammingweight((n+1)^2) && #binary(n^2)==#binary((n+1)^2) \\ Charles R Greathouse IV, Aug 29 2015

Extensions

a(27)-a(54) from Charles R Greathouse IV, Aug 29 2015