A116367 Sums of rows of the triangle in A116366.

6, 18, 36, 70, 104, 158, 208, 282, 388, 468, 602, 728, 838, 984, 1174, 1382, 1536, 1772, 1986, 2170, 2448, 2698, 3008, 3386, 3684, 3940, 4258, 4530, 4868, 5528, 5910, 6370, 6712, 7340, 7710, 8234, 8776, 9258, 9832, 10424, 10866, 11658, 12128, 12694, 13180

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..n} A116366(n,k).

a(n) = (n+1)*A000040(n+1) + A007504(n) - 2.

Mathematica

Table[Sum[Prime[n+1] + Prime[k+1], {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, May 18 2019 *)

Prog

(PARI) vector(50, n, sum(k=1, n, prime(n+1) + prime(k+1))) \\ G. C. Greubel, May 18 2019
(Magma) [(&+[NthPrime(n+1) + NthPrime(k+1): k in [1..n]]): n in [1..50]]; // G. C. Greubel, May 18 2019
(Sage) [sum(nth_prime(n+1) + nth_prime(k+1) for k in (1..n)) for n in (1..50)] # G. C. Greubel, May 18 2019
(GAP) List([1..50], n-> Sum([1..n], k-> Primes[n+1] + Primes[k+1])) # G. C. Greubel, May 18 2019

Crossrefs

Sequence in context: A295026 A034857 A372847 * A225384 A276480 A180438

Adjacent sequences: A116364 A116365 A116366 * A116368 A116369 A116370

Keyword

nonn

Author

Reinhard Zumkeller, Feb 06 2006

Status

approved