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

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, 20, 21, 22, 23, 24, 25, 24, 25, 26, 27, 28, 29, 30, 31, 30, 31, 32, 33, 34, 35, 36, 37, 36, 37, 38, 39, 40, 41, 42, 43, 42, 43, 44, 45, 46, 47, 48, 49, 48, 49, 50, 51, 52, 53, 54, 55

Offset: 1

Author

Benoit Cloitre, Jun 14 2002

Keywords

• easy
• nonn

Examples

			Because 53-1 = 52 is not congruent to 1 (mod 8); a(71) = 71 - 2*ceiling(71/8) = 71 - 2*9 = 53.
		

Links

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

Crossrefs

Cf. A071932, A071933.

Partial sums of A071936.

Programs

Mathematica

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

PARI

for(n=1,100,print1(sum(i=1,n,kronecker(i+1,i)),","))

Sage

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

Formula

a(n) = n - 2*ceiling(n/8) + 2 if n == 1 (mod 8) a(n) = n - 2*ceiling(n/8) otherwise.