A060108 Sequence of sums based on primes = 7 mod 8.

2, 22, 40, 92, 210, 260, 442, 672, 950, 1162, 1520, 1650, 2072, 2380, 2882, 3060, 4030, 5370, 5612, 6112, 7740, 8030, 8932, 9560, 9882, 10542, 14950, 15352, 16590, 17442, 21540, 22022, 23002, 23500, 28222, 29330, 31032, 32782, 34580, 35190

Offset

1,1

Links

Table of n, a(n) for n=1..40.

C. Popescu, Problem 10852, American Mathematical Monthly, Vol. 108 (2001), p. 171.

C. Popescu, Roy Barbara and Omran Kouba, A Sum Related to Quadratic Residues: 10852, American Mathematical Monthly, Vol. 109 (2002), p. 208.

Formula

a(n) = Sum_{k=1..(p-1)/2} floor(k^2/p+1/2) where p is n-th prime congruent to 7 mod 8 (i.e. A007522(n)).

a(n) = (A007522(n)^2 - 1)/24. See 2nd link. - Michel Marcus, Dec 12 2017

Example

For n=2, p=A007522(2)=23, so a(2)=0+0+0+1+1+2+2+3+4+4+5=22.

Prog

(PARI) lista(nn) = {forprime(p=2, nn, if ((p % 8) == 7, print1((p^2-1)/24, ", ")); ); } \\ Michel Marcus, Dec 12 2017

Crossrefs

Cf. A007522.

Sequence in context: A227534 A126913 A019593 * A221762 A154798 A350318

Adjacent sequences: A060105 A060106 A060107 * A060109 A060110 A060111

Keyword

easy,nonn

Author

Marc LeBrun, Feb 27 2001

Status

approved