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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
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
Sequence in context: A071993 A317754 A317854 * A118777 A073068 A166006
KEYWORD
nonn,look
AUTHOR
Altug Alkan, Aug 05 2018
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)