A322997 -id:A322997 - cp's OEIS frontend

A322996 Number of iterations of A049820(x) = x - A000005(x) needed to reach an odd number or zero, when starting from x = n.

0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 3, 0, 3, 0, 4, 0, 1, 0, 4, 0, 5, 0, 5, 0, 2, 0, 6, 0, 6, 0, 6, 0, 7, 0, 7, 0, 1, 0, 8, 0, 8, 0, 8, 0, 9, 0, 9, 0, 9, 0, 10, 0, 10, 0, 10, 0, 10, 0, 11, 0, 10, 0, 12, 0, 1, 0, 12, 0, 13, 0, 13, 0, 11, 0, 14, 0, 14, 0, 14, 0, 14, 0, 15, 0, 12, 0, 16, 0, 15, 0, 15, 0, 17, 0, 16, 0, 13, 0, 18, 0, 1, 0, 17, 0, 14, 0

Offset: 0

Antti Karttunen, Jan 05 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..110880

Cf. A000005, A049820, A155043, A259934, A322987, A322997 (bisection), A323073.

Cf. also A322983.

A322996[n_] := A322996[n] = If[n == 0 || OddQ[n], 0, 1 + A322996[n - DivisorSigma[0, n]]];
Array[A322996, 100, 0] (* Paolo Xausa, Jan 15 2025 *)

A322996(n) = if((!n)||(n%2),0,1+A322996(n-numdiv(n)));

A322996(n) = { for(j=0,oo,if((!n)||(n%2),return(j)); n -= numdiv(n)); };

a(0) = 0; for n >= 1, for n odd, a(n) = 0, and for n even, a(n) = 1 + a(n-A000005(n)).
a(n) <= A155043(n).
For n >= 83, a(2*n) = 1+A322987(2*n).

A322984 Number of iterations of A011371(x) = x - A000120(x) needed to reach an odd number, when starting from x = 2n.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 3, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 3, 2, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 2, 1, 3, 1, 1, 4, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 3, 2, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 2, 1, 3, 1, 1, 4, 5, 1, 1, 2, 1, 3, 2, 1, 1, 2

Offset: 1

Antti Karttunen, Jan 05 2019

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n

Bisection of A322983.
Cf. A000120, A011371.
Cf. also A322997.

A011371(n) = (n - hammingweight(n));
A322983(n) = if((n%2),0,1+A322983(A011371(n)));
A322984(n) = A322983(n+n);

a(n) = A322983(2*n).

cp's OEIS Frontend

A322996 Number of iterations of A049820(x) = x - A000005(x) needed to reach an odd number or zero, when starting from x = n.

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A322984 Number of iterations of A011371(x) = x - A000120(x) needed to reach an odd number, when starting from x = 2n.

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