A283025 Remainder when sum of first n terms of A005185 is divided by n.

0, 0, 1, 3, 0, 2, 5, 0, 3, 6, 9, 2, 6, 10, 1, 5, 10, 16, 3, 9, 15, 21, 4, 13, 20, 1, 9, 17, 25, 3, 14, 22, 30, 7, 18, 27, 0, 11, 21, 32, 3, 14, 26, 38, 5, 16, 27, 46, 8, 19, 35, 49, 8, 23, 38, 51, 11, 25, 41, 57, 12, 27, 50, 2, 15, 35, 52, 67, 19, 40, 58, 5, 25, 44, 64, 7, 28, 47, 67, 9, 31, 52, 73, 13, 34, 56, 80, 16, 38, 62, 86, 18

Offset: 1

Author

Altug Alkan, Feb 27 2017

Keywords

• nonn
• look

Comments

Numbers n such that a(n) = 0 are 1, 2, 5, 8, 37, 99, 1580, 42029, ...

Sequence is a mixture of regularity and irregularity. - Douglas Hofstadter, Mar 03 2017

Examples

			a(4) = 3 since Sum_{k=1..4} A005185(k) = 1 + 1 + 2 + 3 = 7 and remainder when 7 is divided by 4 is 3.
		

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000
• Altug Alkan, Alternative Graph of A283025
• Altug Alkan, Illustration Of Residue Classes Modulo 4

Crossrefs

Cf. A005185, A076268, A282891, A282894.

Programs

Maple

A005185:= proc(n) option remember; procname(n-procname(n-1)) +procname(n-procname(n-2)) end proc:
A005185(1):= 1: A005185(2):= 1:
L:= ListTools[PartialSums](map(A005185, [$1..1000])):
seq(L[i] mod i, i=1..1000); # Robert Israel, Feb 28 2017

Mathematica

h[1]=h[2]=1; h[n_]:=h[n]= h[n-h[n-1]] + h[n-h[n-2]]; Mod[ Accumulate[h /@ Range[100]], Range[100]] (* Giovanni Resta, Feb 27 2017 *)

PARI

a=vector(1000); a[1]=a[2]=1; for(n=3, #a, a[n]=a[n-a[n-1]]+a[n-a[n-2]]); vector(#a, n, sum(k=1, n, a[k]) % n)

PARI

first(n)=my(v=vector(n), s); v[1]=v[2]=1; for(k=3, n, v[k]=v[k-v[k-1]]+v[k-v[k-2]]); for(k=1, n, s+=v[k]; v[k]=s%k); v \\ after Charles R Greathouse IV at A282891

Formula

a(n) = (Sum_{k=1..n} A005185(k)) mod n.

a(n) = A076268(n) mod n.