A115831 Numbers k such that 9*k XOR 16*k = 25*k, or equally, that 9*k AND 16*k = 0, where AND is bitwise-and.

0, 1, 2, 4, 5, 8, 10, 16, 20, 32, 33, 40, 64, 65, 66, 80, 128, 129, 130, 132, 133, 143, 160, 161, 256, 257, 258, 260, 261, 264, 266, 285, 286, 320, 321, 322, 512, 513, 514, 516, 517, 520, 522, 528, 532, 569, 570, 572, 573, 640, 641, 642, 644, 645, 655, 1024

Offset

1,3

Comments

If n is a term, then 2*n is also a term, and vice versa.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences defined by congruent products under XOR.

Index entries for sequences related to binary expansion of n.

Example

143 = "10001111" (in binary, A007088(143)), when multiplied by 9, gives:
.
     11111     (carry bits)
   10001111    = 8*143
      10001111 = 143
--------------
   10100000111 = 1287 = 8*143 + 143 = 9*143
  10001111     = (16*143)
--------------
  110111110111 = 1287 XOR 16*143 = 1287 + 16*143 = 3575 = 16*k + 8*k + k (= 25*k) as (1287 AND 16*143) = 0, and therefore 143 is included in this sequence.

Mathematica

Select[Range[0, 1100], BitXor[9#, 16#]==25#&] (* Harvey P. Dale, Mar 22 2012 *)

Prog

(PARI) is(n)=bitxor(9*n, 16*n)==25*n \\ Charles R Greathouse IV, Sep 25 2024
(PARI) is_A115831(n) = !bitand(9*n, 16*n); \\ Antti Karttunen, Dec 22 2025

Crossrefs

Cf. A003987, A004198, A115832 (terms shown in binary).

Cf. A391737 (subsequence).

Cf. also A115422.

Sequence in context: A133075 A018433 A228939 * A391737 A094958 A018565

Adjacent sequences: A115828 A115829 A115830 * A115832 A115833 A115834

Keyword

nonn,base

Author

Antti Karttunen, Feb 01 2006

Extensions

An alternative definition added to the name, starting offset corrected, and also an example was written by Antti Karttunen, Dec 22 2025

Status

approved