A282894 Remainder when sum of first n terms of A004001 is divided by A004001(n).

0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 4, 4, 6, 6, 6, 6, 6, 7, 9, 0, 0, 2, 5, 5, 8, 8, 8, 10, 10, 10, 10, 10, 9, 9, 10, 12, 15, 15, 18, 22, 3, 3, 7, 12, 12, 17, 17, 17, 21, 26, 26, 1, 1, 1, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 2, 0, 34, 35, 0, 2, 2, 4, 7, 11, 16, 16, 21, 27, 34, 34, 41, 2, 2, 9, 9, 9, 15, 22, 30, 30, 38, 47, 47, 2, 2, 2

Offset

1,10

Links

Altug Alkan, Table of n, a(n) for n = 1..10000

Altug Alkan, Alternative Graph of A282894

Formula

a(n) = (Sum_{k=1..n} A004001(k)) mod A004001(n).

Example

a(6) = 1 since Sum_{k=1..6} A004001(k) = 1 + 1 + 2 + 2 + 3 + 4 = 13 and remainder when 13 is divided by A004001(6) = 4 is 1.

Maple

A004001:= proc(n) option remember; procname(procname(n-1)) +procname(n-procname(n-1)) end proc:
A004001(1):= 1: A004001(2):= 1:
L:= ListTools[PartialSums](map(A004001, [$1..1000])):
seq(L[i] mod A004001(i), i=1..1000); # Robert Israel, Feb 26 2017

Mathematica

a[1] = 1; a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; MapIndexed[Last@ QuotientRemainder[#1, a@ First@ #2] &, Accumulate@ Table[a@ n, {n, 96}]] (* Michael De Vlieger, Feb 24 2017, after Robert G. Wilson v at A004001 *)

Prog

(PARI) a=vector(1000); a[1]=a[2]=1; for(n=3, #a, a[n]=a[a[n-1]]+a[n-a[n-1]]); vector(#a, n, sum(k=1, n, a[k]) % a[n])
(PARI) first(n)=my(v=vector(n), s); v[1]=v[2]=1; for(k=3, n, v[k]=v[v[k-1]]+v[k-v[k-1]]); for(k=1, n, s+=v[k]; v[k]=s%v[k]); v \\ Charles R Greathouse IV, Feb 26 2017

Crossrefs

Cf. A004001, A282891.

Sequence in context: A348769 A058043 A251546 * A162550 A191682 A113724

Adjacent sequences: A282891 A282892 A282893 * A282895 A282896 A282897

Keyword

nonn,look

Author

Altug Alkan, Feb 24 2017

Status

approved