A090396 Remainder when the sum of the first n primes is divided by n.

0, 1, 1, 1, 3, 5, 2, 5, 1, 9, 6, 5, 4, 1, 13, 13, 15, 15, 17, 19, 19, 21, 0, 3, 10, 17, 22, 27, 1, 3, 15, 27, 8, 19, 1, 15, 31, 11, 28, 7, 27, 3, 26, 3, 23, 41, 20, 5, 37, 17, 46, 25, 0, 33, 13, 49, 30, 7, 43, 19, 52, 29, 14, 61, 41, 19, 5, 59, 50, 37, 22, 7, 67, 55, 43, 29, 15, 3, 68, 57

Offset

1,5

Comments

a(n) = 0 if and only if n is a term of A045345. - Nicholas Drozd, Nov 18 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Karl-Heinz Hofmann, Listening to the terms of A090396, YouTube video.

Karl-Heinz Hofmann, Plot of 3 selected ranges, n = 1..8200, 59000..113000, 105000..154000.

Hugo Pfoertner, Visualization of a(n)/n, covering time range of audio track in video (160000 terms).

Hugo Pfoertner, Filtered spectrum of a(n)/n waveform, shifted to audible frequency range.

Formula

a(n) = A007504(n) mod n. - Karl-Heinz Hofmann, May 05 2021

Maple

N:= 1000; # to get the first N terms
pN:= ithprime(N):
C:= map(round, Statistics:-CumulativeSum(select(isprime, [$1..pN])));
seq(C[n] mod n, n = 1 .. N); # Robert Israel, May 29 2014

Mathematica

t = Table[Mod[ Sum[Prime[i], {i, 1, n}], n], {n, 1, 100}]
Module[{nn=80, pr}, pr=Accumulate[Prime[Range[nn]]]; Table[Mod[pr[[n]], n], {n, nn}]] (* Harvey P. Dale, Jul 03 2019 *)

Prog

(PARI) a(n) = sum(k=1, n, prime(k)) % n;
for(n=1, 80, print1(a(n), ", ")); \\ Indranil Ghosh, Mar 06 2017

Crossrefs

Cf. A007504 (sum of first n primes), A045345 (indices of 0's).

Cf. A060620 (corresponding floor quotients).

Sequence in context: A065188 A065257 A258428 * A086387 A073264 A198099

Adjacent sequences: A090393 A090394 A090395 * A090397 A090398 A090399

Keyword

nonn,look

Author

Joseph L. Pe, Jan 31 2004

Status

approved