A359508 - OEIS

A359508

a(n) = log_2(A359507(n) - 1).

0, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2

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OFFSET

1,5

COMMENTS

Conjecture: A359507(n) is always of the form 2^m + 1.

If log_2(A359507(n) - 1) is not an integer, then define a(n) = -1.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(n) = A000523(A359507(n)-1).

Conjecture:

a(1) = 0,

a(2) = 1,

a(3) = 1,

a(4k) = 1 for k > 0,

a(4k+1) = 2 for k > 0,

a(4k+2) = 1 for k > 0,

a(4k+3) = a(k) + 2 for k > 0.

Apparently, a(n) = abs(A378218(1+n)). [This holds at least up to n=65537] - Antti Karttunen, Nov 22 2024

PROG

(PARI)

A359506(n) = if(n==0, return (0), my (x=[n], y); for (m=n+1, oo, if (vecmin(y=[bitxor(v, m) | v<-x])==0, return (m), x=setunion(x, Set(y))))); \\ From A359506.

A359507(n) = (A359506(n)-n);

A359508(n) = (#digits(A359507(n)-1, 2)-1); \\ Antti Karttunen, Nov 22 2024

CROSSREFS

Cf. A000523, A359506, A359507, A378218.

Sequence in context: A327925 A320012 A378218 * A352825 A241276 A325759

Adjacent sequences: A359505 A359506 A359507 * A359509 A359510 A359511

KEYWORD

nonn,changed

AUTHOR

Peter Kagey, Jan 03 2023

EXTENSIONS

More terms from Antti Karttunen, Nov 22 2024

STATUS

approved