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
Keywords
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
Crossrefs
Programs
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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);
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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 *)
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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)
Extensions
More than the usual number of terms are displayed in order to go out beyond the long initial 0,1 subsequence.
Comments