

A090396


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


6



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
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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
KarlHeinz Hofmann, Listening to the terms of A090396, YouTube video.
KarlHeinz 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.  KarlHeinz 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



