A071933 a(n) = Sum_{i=1..n} K(i,i+1), where K(x,y) is the Kronecker symbol (x/y).

1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 3, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 7, 8, 9, 8, 7, 8, 9, 8, 9, 10, 11, 10, 11, 12, 13, 12, 13, 14, 15, 14, 13, 14, 15, 14, 13, 14, 15, 14, 15, 16, 17, 16, 15, 16, 17, 16, 15, 16, 17, 16, 17, 18, 19, 18, 19, 20, 21, 20, 21, 22, 23, 22, 21, 22, 23, 22, 23

Offset

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

a(n) = n/4 + O(n), asymptotically. [Perhaps O(n) should be o(n)? - N. J. A. Sloane, Mar 26 2019]

In fact we have a(n) = n/4 + O(log(n)). More precisely let c(n)=A037800(n) then we get a(8n)=2n+2+2c(n), a(8n+1)=2n+3+2c(n), a(8n+2)=2n+2+2c(n), a(8n+3)=2n+2+2c(n)+(-1)^n, a(8n+4)=2n+3+2c(n)+(-1)^n, a(8n+5)=2n+4+2c(n)+(-1)^n, a(8n+6)=2n+3+2c(n)+(-1)^n, a(8n+7)=2n+3+2c(n+1). - Benoit Cloitre, Mar 30 2019

Mathematica

Table[Sum[KroneckerSymbol[j, j+1], {j, 1, n}], {n, 1, 80}] (* G. C. Greubel, Mar 17 2019 *)

Prog

(PARI) for(n=1, 100, print1(sum(i=1, n, kronecker(i, i+1)), ", "))
(Sage) [sum(kronecker_symbol(j, j+1) for j in (1..n)) for n in (1..80)] # G. C. Greubel, Mar 17 2019

Crossrefs

Cf. A071932, A071934.

Sequence in context: A213183 A125929 A309236 * A209802 A064672 A138554

Adjacent sequences: A071930 A071931 A071932 * A071934 A071935 A071936

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 14 2002

Status

approved