

A071934


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


3



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
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OFFSET

1,4


LINKS

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


FORMULA

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


EXAMPLE

Because 531 = 52 is not congruent to 1 (mod 8); a(71) = 71  2*ceiling(71/8) = 71  2*9 = 53.


MATHEMATICA

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


PROG

(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


CROSSREFS

Cf. A071932, A071933.
Sequence in context: A279513 A000026 A005599 * A161658 A066853 A264856
Adjacent sequences: A071931 A071932 A071933 * A071935 A071936 A071937


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, Jun 14 2002


STATUS

approved



