

A282891


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


6



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
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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(n1)) +procname(nprocname(n1)) 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[k1]]+v[kv[k1]]); 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: A173658 A277618 A219250 * A117137 A002344 A011233
Adjacent sequences: A282888 A282889 A282890 * A282892 A282893 A282894


KEYWORD

nonn,look


AUTHOR

Altug Alkan, Feb 24 2017


STATUS

approved



