A071932 a(n) = 4*Sum_{i=1..n} K(i,i+1) - n, where K(x,y) is the Kronecker symbol (x/y).

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

Offset: 3

Author

Benoit Cloitre, Jun 14 2002

Keywords

• easy
• nonn

Comments

a(n) > 0 for n > 2 and it seems that a(n)/log(n) is bounded: a(n) < 4*log(n) for n sufficiently large. Does lim_{n->infinity} a(n)/log(n) exist?

Links

• G. C. Greubel, Table of n, a(n) for n = 3..5000

Crossrefs

Cf. A071933, A071934.

Programs

Mathematica

Table[4*Sum[KroneckerSymbol[j, j+1], {j, n}] - n, {n, 3, 80}] (* G. C. Greubel, Mar 17 2019 *)

PARI

for(n=3,100,print1(4*sum(i=1,n,kronecker(i,i+1))-n,","))

Sage

[4*sum(kronecker_symbol(j+1,j) for j in (1..n))-n for n in (3..80)] # G. C. Greubel, Mar 17 2019