A283525 Remainder when sum of first n terms of A004001 is divided by 3*n.

1, 2, 4, 6, 9, 13, 17, 21, 26, 2, 6, 10, 15, 20, 25, 30, 36, 43, 51, 0, 6, 13, 21, 29, 38, 47, 56, 66, 76, 86, 3, 10, 18, 27, 37, 48, 60, 72, 85, 99, 114, 3, 16, 30, 44, 59, 74, 89, 105, 122, 139, 1, 16, 31, 47, 63, 79, 95, 112, 129, 146, 163, 180, 5, 20, 36, 53, 71, 90, 110, 130, 151, 173, 196, 220, 16, 38, 61, 85, 109

Offset: 1

Author

Altug Alkan, Mar 10 2017

Keywords

• nonn

Comments

Sequence represents b(n, 3) where b(n, i) = (Sum_{k=1..n} A004001(k)) mod (n*i). See also A282891, A283501 and corresponding illustrations in Links section.

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000
• Altug Alkan, Illustration of Residue Classes Modulo 12
• Altug Alkan, Alternative Scatterplot of A283525

Crossrefs

Cf. A004001, A282891, A283501.

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 (3*i), i=1..1000); # after Robert Israel at A282891

Mathematica

b[1] = 1; b[2] = 1; b[n_] := b[n] = b[b[n - 1]] + b[n - b[n - 1]]; a[n_] := Mod[Sum[b[k], {k, n}], 3 n]; Array[a, 80] (* Robert G. Wilson v, Mar 13 2017 *)

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]) % (3*n))

Formula

a(n) = (Sum_{k=1..n} A004001(k)) mod (3*n).