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

1,1

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.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A164887 A328016 A335796 * A275543 A111733 A127193

Adjacent sequences: A260474 A260475 A260476 * A260478 A260479 A260480

Keyword

base,easy,nonn

Author

Dhilan Lahoti, Aug 28 2015

Extensions

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

Status

approved