A317754 Let b(1) = b(2) = 1; for n >= 3, b(n) = n - b(t(n)) - b(n-t(n)) where t = A004001. a(n) = 2*b(n) - n.

1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, -2, -1, 0, -1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, -1, 0, -1, -2, -3, -4, -3, -2, -1, 0, -1, -2, -3, -4, -5, -6, -5, -4, -3, -2, -1, 0, -1, -2, -3, -4, -3, -2, -1, 0, -1, 0, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0

Offset

1,12

Links

Altug Alkan, Table of n, a(n) for n = 1..32768

Maple

t:= proc(n) option remember; `if`(n<3, 1,
      t(t(n-1)) +t(n-t(n-1)))
    end:
b:= proc(n) option remember; `if`(n<3, 1,
      n -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, a[[a[[-1]] ]] + a[[-a[[-1]] ]] ] ] @@ {#, Length@ # + 1} &, {1, 1}, Last@ # < 60 &], b}, b = NestWhile[Function[{b, n}, Append[b, n - b[[t[[n]] ]] - b[[-t[[n]] ]] ] ] @@ {#, Length@ # + 1} &, {1, 1}, Length@ # < Length@ t &]; Array[2 b[[#]] - # &, Length@ b] ] (* Michael De Vlieger, Aug 07 2018 *)

Prog

(PARI) t=vector(99); t[1]=t[2]=1; for(n=3, #t, t[n] = t[n-t[n-1]]+t[t[n-1]]); b=vector(99); b[1]=b[2]=1; for(n=3, #b, b[n] = n-b[t[n]]-b[n-t[n]]); vector(99, k, 2*b[k]-k)

Crossrefs

Cf. A004001, A004074, A317648, A317742.

Sequence in context: A308343 A331216 A071993 * A317854 A317742 A118777

Adjacent sequences: A317751 A317752 A317753 * A317755 A317756 A317757

Keyword

sign,look,hear

Author

Altug Alkan, Aug 06 2018

Status

approved