A061802 Sum of n-th row of triangle of primes: 2; 2 3 2; 2 3 5 3 2; 2 3 5 7 5 3 2; ...; where n-th row contains 2n+1 terms.

2, 7, 15, 27, 45, 69, 99, 135, 177, 229, 289, 357, 435, 519, 609, 709, 821, 941, 1069, 1207, 1351, 1503, 1665, 1837, 2023, 2221, 2425, 2635, 2851, 3073, 3313, 3571, 3839, 4115, 4403, 4703, 5011, 5331, 5661, 6001, 6353, 6713, 7085, 7469, 7859, 8255, 8665

Offset: 0

Author

Amarnath Murthy, May 28 2001

Keywords

• nonn
• easy

Comments

Row sums of A138143. - Omar E. Pol, Feb 13 2014

For n = 3..9, a(n) = 3*(n^2 - 3*n + 5). - Nicholas Drozd, Apr 10 2021

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Harry J. Smith)

Crossrefs

Cf. A001043 (first differences), A007504, A138143.

Partial sums of A011974.

Programs

Mathematica

Accumulate[Join[{2},ListConvolve[{1,1},Prime[Range[100]]]]] (* Paolo Xausa, Oct 31 2023 *)

PARI

{ n=-1; a=q=0; forprime (p=2, prime(1001), write("b061802.txt", n++, " ", a+=p + q); q=p ) } \\ Harry J. Smith, Jul 28 2009

Formula

a(n) = a(n-1) + prime(n) + prime(n-1).

a(n) = A007504(n) + A007504(n+1) so we have the asymptotic expansion a(n) ~ n^2*log(n). - Henry Bottomley, May 30 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 29 2001