A262744 -id:A262744 - cp's OEIS frontend

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

Altug Alkan, Feb 11 2017

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

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

Altug Alkan, Table of n, a(n) for n = 1..10000
Altug Alkan, Alternative Illustration of A282282

Cf. A000040, A000330, A024450, A262744.

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

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

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

A263559 a(n) = A083186(n) mod A007504(n).

Original entry on oeis.org

1, 3, 9, 2, 11, 26, 51, 3, 17, 39, 73, 119, 175, 237, 307, 8, 49, 88, 151, 220, 295, 380, 479, 584, 705, 848, 999, 1158, 1321, 1486, 1687, 51, 139, 241, 355, 477, 611, 763, 919, 1085, 1253, 1435, 1633, 1839, 2055, 2277, 2519, 2813, 3111, 3413, 3719, 4023, 4341, 4683, 5019

Offset: 1

Altug Alkan, Oct 21 2015

nonn

Sequence is interesting because of its graph. a(n)-a(n-1) < 0 at some points such as n=4 and n=8, although usually a(n)-a(n-1) > 0.

			a(1) = 1 because prime(prime(1)) mod prime(1) = 3 mod 2 = 1.

Cf. A007504, A083186, A262744.

Table[Mod[Sum[Prime@ Prime@ k, {k, n}], Sum[Prime@ k, {k, n}]], {n, 55}] (* Michael De Vlieger, Oct 21 2015 *)

vector(100, n, sum(k=1, n, prime(prime(k))) % sum(k=1, n, prime(k)))

cp's OEIS Frontend

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

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