A263078 a(n) = greatest k for which A155043(n+k) < A155043(n); a(n) = A263077(n)-n.

-1, -2, -1, -2, 1, -4, 5, -2, -3, -4, 1, -6, 5, -2, 3, 2, 5, -6, 11, -2, 9, -4, 11, -2, -3, -4, 15, -6, 19, -8, 29, -2, 27, -4, 37, 12, 47, -4, 45, -6, 55, -8, 65, -2, 51, -4, 61, -6, -1, -2, 69, -4, 79, -6, 77, -8, 83, 2, 81, -12, 79, 10, 77, 76, 75, 6, 73, 16, 71, 14, 69, -12, 67, 22, 65, 20, 73, 18, 77, 16, 27, 26, 37, -12, 35, 34, 45, 20, 51, 18, 49, 40, 47, 26, 45, -12, 43, 42, 41, 40, 39, 30

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..124340

Formula

a(n) = A263077(n)-n.

Example

For n=1 we have A049820(1) = 0, thus A155043(1) = 1, and 0 is the only (and thus the largest) number from which zero can be reached with less steps (namely in zero steps, A155043(0) = 0), thus a(1) = 0 - 1 = -1.
For n=7, we have A155043(7) = 4 [as A049820(7) = 5, A049820(5) = 3, A049820(3) = 1, A049820(1) = 0], but there exists x=12 for which we have A049820(12) = 6, A049820(6) = 2, A049820(2) = 0, and this is the largest x such that A155043(x) < A155043(7), thus a(7) = 12 - 7 = 5.

Mathematica

a[0] = 0; a[n_] := a[n] = 1 + a[n - DivisorSigma[0, n]]; Table[k = 3 n;
While[a@ k >= a@ n, k--]; k - n, {n, 102}] (* Michael De Vlieger, Oct 13 2015 *)

Prog

(PARI)
A263078 = n -> A263077(n) - n;
for(n=1, 124340, write("b263078.txt", n, " ", A263078(n)));
\\ Other code as in A263077

Crossrefs

Cf. A155043, A261089, A262503, A262909, A263077.

Cf. A263079 (indices of the negative terms), A263080 (of the positive terms).

Sequence in context: A166235 A143591 A085063 * A329869 A331188 A058511

Adjacent sequences: A263075 A263076 A263077 * A263079 A263080 A263081

Keyword

sign

Author

Antti Karttunen, Oct 09 2015

Status

approved