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

1,4

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

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

Formula

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

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A005185, A076268, A282891, A282894.

Sequence in context: A261163 A292244 A208329 * A089598 A117139 A159959

Adjacent sequences: A283022 A283023 A283024 * A283026 A283027 A283028

Keyword

nonn,look

Author

Altug Alkan, Feb 27 2017

Status

approved