A282891 Remainder when sum of first n terms of A004001 is divided by n.

0, 0, 1, 2, 4, 1, 3, 5, 8, 2, 6, 10, 2, 6, 10, 14, 2, 7, 13, 0, 6, 13, 21, 5, 13, 21, 2, 10, 18, 26, 3, 10, 18, 27, 2, 12, 23, 34, 7, 19, 32, 3, 16, 30, 44, 13, 27, 41, 7, 22, 37, 1, 16, 31, 47, 7, 22, 37, 53, 9, 24, 39, 54, 5, 20, 36, 53, 3, 21, 40, 59, 7, 27, 48, 70, 16, 38, 61, 6, 29, 53, 78, 20, 45, 70, 9, 34, 60, 87, 24

Offset

1,4

Comments

Numbers n such that a(n) = 0 are 1, 2, 20, 4743, 10936, ...

Links

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

Altug Alkan, Alternative Scatterplot of A282891

Altug Alkan, Illustration Of Residue Classes Modulo 4

Formula

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

Example

a(5) = 4 since Sum_{k=1..5} A004001(k) = 1 + 1 + 2 + 2 + 3 = 9 and remainder when 9 is divided by 5 is 4.

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 i, i=1..1000); # Robert Israel, Feb 24 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, First@ #2] &, Accumulate@ Table[a@ n, {n, 90}]] (* Michael De Vlieger, Feb 24 2017, after Robert G. Wilson v at A004001 *)

Prog

(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%k); v \\ Charles R Greathouse IV, Feb 26 2017

Crossrefs

Cf. A004001, A282894, A283025.

Sequence in context: A358054 A219250 A361643 * A117137 A002344 A011233

Adjacent sequences: A282888 A282889 A282890 * A282892 A282893 A282894

Keyword

nonn,look

Author

Altug Alkan, Feb 24 2017

Status

approved