cp's OEIS Frontend

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

%I A064894 #21 Feb 13 2024 09:57:39
%S A064894 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,
%T A064894 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,
%U A064894 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
%N A064894 Binary dilution of n. GCD of exponents in binary expansion of n.
%C A064894 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)).
%H A064894 Peter Kagey, <a href="/A064894/b064894.txt">Table of n, a(n) for n = 0..10000</a>
%F A064894 If n = 2^e0 + 2^e1 +... then a(n) = GCD(e0, e1, ...).
%F A064894 a(A064896(n)) = A056538(n)
%e A064894 577 = 2^0 + 2^6 + 2^9, GCD(0,6,9) = 3 = a(577).
%t A064894 A064894[n_] := Apply[GCD, Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]] - 1];
%t A064894 Array[A064894, 100, 0] (* _Paolo Xausa_, Feb 13 2024 *)
%o A064894 (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
%Y A064894 Cf. A000079, A064895, A064896, A056538.
%K A064894 base,easy,nonn
%O A064894 0,5
%A A064894 _Marc LeBrun_, Oct 11 2001