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

Author

Marc LeBrun, Feb 27 2001

Keywords

• easy
• nonn

Examples

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

Links

• 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.

Crossrefs

Cf. A007522.

Programs

PARI

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

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