cp's OEIS Frontend

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

%I A090396 #73 Jul 14 2024 03:50:47
%S A090396 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,
%T A090396 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,
%U A090396 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
%N A090396 Remainder when the sum of the first n primes is divided by n.
%C A090396 a(n) = 0 if and only if n is a term of A045345. - _Nicholas Drozd_, Nov 18 2018
%H A090396 Robert Israel, <a href="/A090396/b090396.txt">Table of n, a(n) for n = 1..10000</a>
%H A090396 Karl-Heinz Hofmann, <a href="https://www.youtube.com/watch?v=p-Gigy-c1rg">Listening to the terms of A090396</a>, YouTube video.
%H A090396 Karl-Heinz Hofmann, <a href="/A090396/a090396.pdf">Plot of 3 selected ranges</a>, n = 1..8200, 59000..113000, 105000..154000.
%H A090396 Hugo Pfoertner, <a href="https://www.randomwalk.de/sequences/a090396.pdf">Visualization of a(n)/n</a>, covering time range of audio track in video (160000 terms).
%H A090396 Hugo Pfoertner, <a href="/A090396/a090396.png">Filtered spectrum of a(n)/n waveform</a>, shifted to audible frequency range.
%F A090396 a(n) = A007504(n) mod n. - _Karl-Heinz Hofmann_, May 05 2021
%p A090396 N:= 1000; # to get the first N terms
%p A090396 pN:= ithprime(N):
%p A090396 C:= map(round,Statistics:-CumulativeSum(select(isprime,[$1..pN])));
%p A090396 seq(C[n] mod n, n = 1 .. N); # _Robert Israel_, May 29 2014
%t A090396 t = Table[Mod[ Sum[Prime[i], {i, 1, n}], n], {n, 1, 100}]
%t A090396 Module[{nn=80,pr},pr=Accumulate[Prime[Range[nn]]];Table[Mod[pr[[n]],n],{n,nn}]] (* _Harvey P. Dale_, Jul 03 2019 *)
%o A090396 (PARI) a(n) = sum(k=1, n, prime(k)) % n;
%o A090396 for(n=1, 80, print1(a(n),", ")); \\ _Indranil Ghosh_, Mar 06 2017
%Y A090396 Cf. A007504 (sum of first n primes), A045345 (indices of 0's).
%Y A090396 Cf. A060620 (corresponding floor quotients).
%K A090396 nonn,look
%O A090396 1,5
%A A090396 _Joseph L. Pe_, Jan 31 2004