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 A317742 Let b(1) = b(2) = 1; for n >= 3, b(n) = b(t(n)) + b(n-t(n)) where t = A287422. a(n) = 2*b(n) - n. 3
 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 0, 1, 0, 1, 0, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 5, 6, 5, 4, 3, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 0, 1, 0, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 8, 9, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS This sequence has fractal-like structure as A004074, although there are substantial differences of this sequence based on slow A287422 and b(n) sequences. See plots of this sequence and A004074 in Links section. LINKS Altug Alkan, Table of n, a(n) for n = 1..16384 Altug Alkan, Line plots of a(n) and A004074(n) for n <= 2^15 MAPLE t:= proc(n) option remember; `if`(n<3, 1,       n -t(t(n-1)) -t(n-t(n-1)))     end: b:= proc(n) option remember; `if`(n<3, 1,       b(t(n)) +b(n-t(n)))     end: seq(2*b(n)-n, n=1..100); # after Alois P. Heinz at A317686 MATHEMATICA Block[{t = NestWhile[Function[{a, n}, Append[a, n - a[[a[[-1]] ]] - a[[-a[[-1]] ]] ] ] @@ {#, Length@ # + 1} &, {1, 1}, Last@ # < 10^2 &], b}, b = NestWhile[Function[{b, n}, Append[b, b[[t[[n]] ]] + b[[-t[[n]] ]] ] ] @@ {#, Length@ # + 1} &, {1, 1}, Last@ # < Max@ t &]; Array[2 b[[#]] - # &, Length@ b] ] (* Michael De Vlieger, Aug 07 2018 *) t[n_] := t[n] = If[n<3, 1, n - t[t[n-1]] - t[n - t[n-1]]]; b[n_] := b[n] = If[n<3, 1, b[t[n]] + b[n - t[n]]]; Table[2*b[n] - n, {n, 106}] (* Giovanni Resta, Aug 14 2018 *) PROG (PARI) t=vector(199); t[1]=t[2]=1; for(n=3, #t, t[n] = n-t[n-t[n-1]]-t[t[n-1]]); b=vector(199); b[1]=b[2]=1; for(n=3, #b, b[n] = b[t[n]]+b[n-t[n]]); vector(199, k, 2*b[k]-k) CROSSREFS Cf. A004074, A287422, A317648, A317686. Sequence in context: A071993 A317754 A317854 * A118777 A073068 A166006 Adjacent sequences:  A317739 A317740 A317741 * A317743 A317744 A317745 KEYWORD nonn,look AUTHOR Altug Alkan, Aug 05 2018 STATUS approved

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Last modified June 19 00:04 EDT 2021. Contains 345125 sequences. (Running on oeis4.)