A282282 Remainder when sum of squares of the first n primes is divided by n-th square pyramidal number.

0, 3, 10, 27, 43, 13, 106, 7, 131, 87, 322, 177, 675, 137, 546, 1307, 691, 1496, 266, 1307, 2226, 3627, 902, 2487, 5021, 1585, 3446, 5487, 7276, 9245, 3426, 7275, 11887, 2495, 7546, 12203, 111, 5020, 10094, 16023, 22849, 3565, 10462, 16735, 23144, 28889, 2346, 12907, 23619, 33560, 43632, 6555, 14074, 24587

Offset

1,2

Comments

See also graph of this sequence and compare with the graph of A262744.

Links

Altug Alkan, Table of n, a(n) for n = 1..10000

Altug Alkan, Alternative Illustration of A282282

Formula

a(n) = A024450(n) mod A000330(n).

Example

a(3) = 10 because (2^2 + 3^2 + 5^2) mod (1^2 + 2^2 + 3^2) = 10.

Mathematica

Table[Mod[Total[Prime[Range@ n]^2], Binomial[n + 2, 3] + Binomial[n + 1, 3]], {n, 54}] (* Michael De Vlieger, Feb 11 2017 *)

Prog

(PARI) a(n) = sum(k=1, n, prime(k)^2) % (n*(n+1)*(2*n+1)/6);

Crossrefs

Cf. A000040, A000330, A024450, A262744.

Sequence in context: A110158 A301308 A196232 * A105660 A056681 A192959

Adjacent sequences: A282279 A282280 A282281 * A282283 A282284 A282285

Keyword

nonn,easy

Author

Altug Alkan, Feb 11 2017

Status

approved