cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A071934 a(n) = Sum_{i=1..n} K(i+1,i), where K(x,y) is the Kronecker symbol (x/y).

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%I A071934 #19 Jun 24 2022 22:49:50
%S A071934 1,0,1,2,3,4,5,6,7,6,7,8,9,10,11,12,13,12,13,14,15,16,17,18,19,18,19,
%T A071934 20,21,22,23,24,25,24,25,26,27,28,29,30,31,30,31,32,33,34,35,36,37,36,
%U A071934 37,38,39,40,41,42,43,42,43,44,45,46,47,48,49,48,49,50,51,52,53,54,55
%N A071934 a(n) = Sum_{i=1..n} K(i+1,i), where K(x,y) is the Kronecker symbol (x/y).
%H A071934 G. C. Greubel, <a href="/A071934/b071934.txt">Table of n, a(n) for n = 1..5000</a>
%F A071934 a(n) = n - 2*ceiling(n/8) + 2 if n == 1 (mod 8) a(n) = n - 2*ceiling(n/8) otherwise.
%e A071934 Because 53-1 = 52 is not congruent to 1 (mod 8); a(71) = 71 - 2*ceiling(71/8) = 71 - 2*9 = 53.
%t A071934 Table[Sum[KroneckerSymbol[j+1, j], {j,n}], {n, 80}] (* _G. C. Greubel_, Mar 17 2019 *)
%o A071934 (PARI) for(n=1,100,print1(sum(i=1,n,kronecker(i+1,i)),","))
%o A071934 (Sage) [sum(kronecker_symbol(j+1,j) for j in (1..n)) for n in (1..80)] # _G. C. Greubel_, Mar 17 2019
%Y A071934 Cf. A071932, A071933.
%Y A071934 Partial sums of A071936.
%K A071934 easy,nonn
%O A071934 1,4
%A A071934 _Benoit Cloitre_, Jun 14 2002