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

Author

Altug Alkan, Feb 24 2017

Keywords

• nonn
• look

Examples

			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.
		

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000
• Altug Alkan, Alternative Graph of A282894

Crossrefs

Cf. A004001, A282891.

Programs

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 *)

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

Formula

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