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A370731 a(n) is the least k >= 0 such that F(k) AND n = n (where F(k) denotes A000045(k), the k-th Fibonacci number and AND denotes the bitwise AND operator).

%I A370731 #12 Mar 02 2024 07:05:36
%S A370731 0,1,3,4,5,5,10,10,6,7,16,16,7,7,22,22,8,8,10,10,8,8,10,10,11,11,16,
%T A370731 16,17,17,46,46,9,10,9,10,10,10,10,10,13,13,22,22,17,17,22,22,10,10,
%U A370731 10,10,10,10,10,10,14,14,64,64,17,17,94,94,11,11,15,16,19
%N A370731 a(n) is the least k >= 0 such that F(k) AND n = n (where F(k) denotes A000045(k), the k-th Fibonacci number and AND denotes the bitwise AND operator).
%C A370731 This sequence is well defined (see Comments in A370730).
%H A370731 Paolo Xausa, <a href="/A370731/b370731.txt">Table of n, a(n) for n = 0..10000</a>
%F A370731 a(A000045(k)) = k for any k != 2.
%t A370731 A370731[n_] := Block[{k = -1}, While[BitAnd[Fibonacci[++k], n] != n]; k];
%t A370731 Array[A370731, 100, 0] (* _Paolo Xausa_, Mar 01 2024 *)
%o A370731 (PARI) a(n) = { for (k = 0, oo, if (bitand(fibonacci(k), n)==n, return (k););); }
%Y A370731 Cf. A000045, A370730.
%K A370731 nonn,base
%O A370731 0,3
%A A370731 _Rémy Sigrist_, Feb 28 2024