

A352458


2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k AND n = 0 (where AND denotes the bitwise AND operator).


5



0, 1, 2, 1, 4, 5, 2, 1, 8, 1, 2, 1, 12, 5, 2, 1, 16, 17, 18, 17, 4, 5, 2, 1, 24, 17, 18, 17, 12, 5, 2, 1, 32, 1, 34, 1, 4, 5, 2, 1, 40, 1, 34, 1, 12, 5, 2, 1, 48, 17, 50, 17, 4, 5, 2, 1, 56, 17, 50, 17, 12, 5, 2, 1, 64, 65, 2, 1, 4, 5, 2, 1, 72, 65, 2, 1, 12
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

The idea is to keep the 1's in the binary expansion of a number whose positions are related in some way to that number.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n


FORMULA

a(n) <= n with equality iff n belongs to A335702.
a(n) = n  A309274(n).


EXAMPLE

For n = 42:
 42 = 2^5 + 2^3 + 2^1,
 42 AND 5 = 0,
 42 AND 3 = 2 <> 0,
 42 AND 1 = 0,
 so a(42) = 2^5 + 2^1 = 34.


PROG

(PARI) a(n) = { my (v=0, m=n, k); while (m, m=2^k=valuation(m, 2); if (bitand(n, k)==0, v+=2^k)); v }


CROSSREFS

See A352449, A352450, A352451, A352452 for similar sequences.
Cf. A335702 (fixed points).
Sequence in context: A114158 A248666 A162407 * A132741 A072436 A247503
Adjacent sequences: A352455 A352456 A352457 * A352459 A352460 A352461


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Mar 17 2022


STATUS

approved



