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