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A282894 Remainder when sum of first n terms of A004001 is divided by A004001(n).

%I A282894 #27 Feb 28 2017 16:12:57
%S A282894 0,0,0,0,0,1,1,1,1,2,4,4,6,6,6,6,6,7,9,0,0,2,5,5,8,8,8,10,10,10,10,10,
%T A282894 9,9,10,12,15,15,18,22,3,3,7,12,12,17,17,17,21,26,26,1,1,1,4,4,4,4,5,
%U A282894 5,5,5,5,5,2,0,34,35,0,2,2,4,7,11,16,16,21,27,34,34,41,2,2,9,9,9,15,22,30,30,38,47,47,2,2,2
%N A282894 Remainder when sum of first n terms of A004001 is divided by A004001(n).
%H A282894 Altug Alkan, <a href="/A282894/b282894.txt">Table of n, a(n) for n = 1..10000</a>
%H A282894 Altug Alkan, <a href="/A282894/a282894_1.png">Alternative Graph of A282894</a>
%F A282894 a(n) = (Sum_{k=1..n} A004001(k)) mod A004001(n).
%e A282894 a(6) = 1 since Sum_{k=1..6} A004001(k) = 1 + 1 + 2 + 2 + 3 + 4 = 13 and remainder when 13 is divided by A004001(6) = 4 is 1.
%p A282894 A004001:= proc(n) option remember; procname(procname(n-1)) +procname(n-procname(n-1)) end proc:
%p A282894 A004001(1):= 1: A004001(2):= 1:
%p A282894 L:= ListTools[PartialSums](map(A004001, [$1..1000])):
%p A282894 seq(L[i] mod A004001(i), i=1..1000); # _Robert Israel_, Feb 26 2017
%t A282894 a[1] = 1; a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; MapIndexed[Last@ QuotientRemainder[#1, a@ First@ #2] &, Accumulate@ Table[a@ n, {n, 96}]] (* _Michael De Vlieger_, Feb 24 2017, after _Robert G. Wilson v_ at A004001 *)
%o A282894 (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]) % a[n])
%o A282894 (PARI) first(n)=my(v=vector(n),s); v[1]=v[2]=1; for(k=3, n, v[k]=v[v[k-1]]+v[k-v[k-1]]); for(k=1,n, s+=v[k]; v[k]=s%v[k]); v \\ _Charles R Greathouse IV_, Feb 26 2017
%Y A282894 Cf. A004001, A282891.
%K A282894 nonn,look
%O A282894 1,10
%A A282894 _Altug Alkan_, Feb 24 2017