A362452 Gilbreath transform of {sigma(i)-i, i >= 1} (see sum of aliquot parts, A001065).

0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 62, 0, 12, 0, 3, 0, 2, 0, 25, 1

Offset

1,120

Comments

See A362451 for further information.

The first 50000 terms of the present sequence suggest that the terms are usually 0's and 1's, except for occasional "geysers". See A362458, A362459.

[It would be nice to have plots of larger numbers of initial terms.]

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..50000

N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: Video, Slides, Updates. (Mentions this sequence.)

Paolo Xausa, Table of n, a(n) for n = 1..1000000

Paolo Xausa, Logarithmic scatterplot for n = 1..1000000

Index entries for sequences related to Gilbreath conjecture and transform

Maple

# To get M terms of the Gilbreath transform of s:
GT := proc(s, M) local G, u, i;
u := [seq(s(i), i=1..M)];
G:=[s(1)];
for i from 1 to M-1 do
u:=[seq(abs(u[i+1]-u[i]), i=1..nops(u)-1)];
G:=[op(G), u[1]]; od:
G;
end;
# For the present sequence:
aliq := proc(n) numtheory[sigma](n) - n; end;
GT(aliq, 150);

Mathematica

A362452[nmax_]:=Module[{d=DivisorSigma[1, Range[nmax]]-Range[nmax]}, Join[{0}, Table[First[d=Abs[Differences[d]]], nmax-1]]]; A362452[200] (* Paolo Xausa, May 07 2023 *)

Prog

(PARI)
f(n) = sigma(n) - n
lista(nn) = my(v=apply(f, [1..nn]), list = List(), nb=nn); listput(list, v[1]); for (n=2, nn, nb--; my(w = vector(nb, k, abs(v[k+1]-v[k]))); listput(list, w[1]); v = w; ); Vec(list);
lista(200)

Crossrefs

Cf. A000005, A000040, A000203, A001065, A036262, A361897, A362450, A362451, A362458, A362459.

Sequence in context: A173418 A147667 A022084 * A110823 A058913 A236301

Adjacent sequences: A362449 A362450 A362451 * A362453 A362454 A362455

Keyword

nonn

Author

N. J. A. Sloane, May 03 2023

Extensions

More than the usual number of terms are displayed in order to go out beyond the long initial 0,1 subsequence.

Status

approved