

A282282


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


1



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
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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



