A317742 -id:A317742 - cp's OEIS frontend

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

Altug Alkan, Aug 06 2018

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

Cf. A004001, A004074, A317648, A317742.

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

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 *)

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)

A317854 Let b(1) = b(2) = 1; for n >= 3, b(n) = n - b(t(n)) - b(n-t(n)) where t = A287422. a(n) = 2*b(n) - n.

Original entry on oeis.org

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

Offset: 1

Altug Alkan, Aug 09 2018

A different version of A317742. Similar to A317754.

Altug Alkan, Table of n, a(n) for n = 1..32768
Altug Alkan, Line plot of a(n) for n <= 2^17
Rémy Sigrist, C++ program for A317854

Cf. A287422, A317742, A317754.

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,
      n -b(t(n)) -b(n-t(n)))
    end:
seq(2*b(n)-n, n=1..100); # after Alois P. Heinz at A317686

t[1]=t[2]=1; t[n_] := t[n] = n - t[t[n-1]] - t[n - t[n-1]]; b[1]=b[2]=1; b[n_] := b[n] = n - b[t[n]] - b[n - t[n]]; a[n_] := 2*b[n] - n; Array[a, 95] (* Giovanni Resta, Aug 14 2018 *)

t=vector(99); t[1]=t[2]=1; for(n=3, #t, t[n] = 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)
(C++) See Links section.

abs(a(n)) = A317742(n).

cp's OEIS Frontend

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.

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