A283501 - OEIS

%I #19 Mar 14 2017 00:26:30

%S 1,2,4,6,9,1,3,5,8,12,17,22,2,6,10,14,19,25,32,0,6,13,21,29,38,47,2,

%T 10,18,26,34,42,51,61,2,12,23,34,46,59,73,3,16,30,44,59,74,89,7,22,37,

%U 53,69,85,102,7,22,37,53,69,85,101,117,5,20,36,53,71,90,110,130,7,27

%N Remainder when sum of first n terms of A004001 is divided by 2*n.

%C Sequence represents b(n, 2) where b(n, i) = (Sum_{k=1..n} A004001(k)) mod (n*i). See also A282891 and corresponding illustration in Links section.

%H Altug Alkan, <a href="/A283501/b283501.txt">Table of n, a(n) for n = 1..10000</a>

%H Altug Alkan, <a href="/A283501/a283501.png">Illustration of Residue Classes Modulo 8</a>

%F a(n) = (Sum_{k=1..n} A004001(k)) mod (2*n).

%e a(6) = 1 since Sum_{k=1..6} A004001(k) = 1 + 1 + 2 + 2 + 3 + 4 = 13 and remainder when 13 is divided by 12 is 1.

%p A004001:= proc(n) option remember; procname(procname(n-1)) +procname(n-procname(n-1)) end proc:

%p A004001(1):= 1: A004001(2):= 1:

%p L:= ListTools[PartialSums](map(A004001, [$1..1000])):

%p seq(L[i] mod (2*i), i=1..1000); # after _Robert Israel_ at A282891

%t a[1] = a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; Table[Mod[Total@ Array[a, n], 2 n], {n, 73}] (* _Michael De Vlieger_, Mar 13 2017, after _Robert G. Wilson v_ at A004001 *)

%o (PARI) a=vector(1000); a[1]=a[2]=1; for(n=3, #a, a[n]=a[a[n-1]]+a[n-a[n-1]]); vector(#a, n, sum(k=1, n, a[k]) % (2*n))

%Y Cf. A004001, A282891.

%K nonn

%O 1,2

%A _Altug Alkan_, Mar 09 2017