A064894 Binary dilution of n. GCD of exponents in binary expansion of n.

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

Offset

0,5

Comments

All bits of n in positions not divisible by a(n) are zero. Hence n in binary contains blocks of a(n)-1 "diluting" 0's (for n>1). Also for n>1, a(2^n) = a(2^n + 1) = n. For i,j odd, a(ij) = GCD(a(i),a(j)).

Links

Peter Kagey, Table of n, a(n) for n = 0..10000

Formula

If n = 2^e0 + 2^e1 +... then a(n) = GCD(e0, e1, ...).

a(A064896(n)) = A056538(n)

Example

577 = 2^0 + 2^6 + 2^9, GCD(0,6,9) = 3 = a(577).

Mathematica

A064894[n_] := Apply[GCD, Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]] - 1];
Array[A064894, 100, 0] (* Paolo Xausa, Feb 13 2024 *)

Prog

(PARI) a(n) = if (n==0, 0, my(ve = select(x->x==1, Vecrev(binary(n)), 1)); gcd(vector(#ve, k, ve[k]-1))); \\ Michel Marcus, Apr 12 2016

Crossrefs

Cf. A000079, A064895, A064896, A056538.

Sequence in context: A198380 A361025 A152805 * A003638 A094267 A136480

Adjacent sequences: A064891 A064892 A064893 * A064895 A064896 A064897

Keyword

base,easy,nonn

Author

Marc LeBrun, Oct 11 2001

Status

approved