A334798 Numbers k such that the binary digits of k*(k-1) and k*(k+1) have the same numbers of 0's and the same number of 1's.

7, 15, 25, 31, 43, 48, 54, 63, 80, 84, 87, 110, 113, 127, 142, 144, 147, 162, 171, 172, 177, 183, 185, 197, 199, 203, 216, 217, 221, 226, 227, 232, 234, 238, 243, 255, 275, 281, 290, 301, 303, 308, 317, 322, 323, 329, 340, 343, 349, 355, 367, 370, 377, 389, 391, 402, 411, 418, 423, 426, 427, 432

Offset

1,1

Comments

k such that A023416(k*(k-1)) = A023416(k*(k+1)) and A000120(k*(k-1))=A000120(k*(k+1)).

Either of A023416 and A000120 could be replaced by A070939 in this condition.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3)=25 is in the sequence because 25*24=600=1001011000_2 and 25*26=650=1010001010_2 both have 6 binary digits 0 and 4 binary digits 1.

Maple

filter:= proc(n) local A, B;
A:= convert(n*(n-1), base, 2);
B:= convert(n*(n+1), base, 2);
nops(A)=nops(B) and convert(A, `+`)=convert(B, `+`)
end proc:
select(filter, [$1..1000]);

Mathematica

sn01Q[k_]:=DigitCount[k(k-1), 2, 0]==DigitCount[k(k+1), 2, 0]&&DigitCount[k(k-1), 2, 1] == DigitCount[ k(k+1), 2, 1]; Select[Range[500], sn01Q] (* Harvey P. Dale, May 27 2023 *)

Prog

(PARI) isok(k) = vecsort(binary(k*(k+1))) == vecsort(binary(k*(k-1))); \\ Michel Marcus, May 12 2020

Crossrefs

Cf. A000120, A023416, A070939, A181775.

Includes terms >= 7 of A000225.

Sequence in context: A056119 A329383 A284758 * A211430 A082111 A323483

Adjacent sequences: A334795 A334796 A334797 * A334799 A334800 A334801

Keyword

nonn,base

Author

Robert Israel, May 11 2020

Status

approved