A097505 Triangle read by rows: T(n,k) = Sum_{j=1..k} Prime(n+j-1).

2, 3, 8, 5, 12, 23, 7, 18, 31, 48, 11, 24, 41, 60, 83, 13, 30, 49, 72, 101, 132, 17, 36, 59, 88, 119, 156, 197, 19, 42, 71, 102, 139, 180, 223, 270, 23, 52, 83, 120, 161, 204, 251, 304, 363, 29, 60, 97, 138, 181, 228, 281, 340, 401, 468, 31, 68, 109, 152, 199, 252, 311, 372, 439, 510, 583

Offset: 1

Author

Reinhard Zumkeller, Aug 26 2004

Keywords

• nonn
• tabl

Links

• G. C. Greubel, Rows n = 1..100 of triangle, flattened

Programs

Magma

[&+[NthPrime(n+j-1): j in [1..k]] : k in [1..n], n in [1..12]]; // G. C. Greubel, Jan 19 2020

Maple

seq(seq( sum(ithprime(n+j-1), j=1..k), k=1..n), n=1..12); # G. C. Greubel, Jan 19 2020

Mathematica

Table[Sum[Prime[n+j-1], {j,k}], {n,12}, {k,n}]//Flatten (* G. C. Greubel, Jan 19 2020 *)

PARI

T(n,k) = sum(j=1,k, prime(n+j-1)); \\ G. C. Greubel, Jan 19 2020

Sage

[[sum(nth_prime(n+j-1) for j in (1..k)) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Jan 19 2020

Formula

T(n,k) = A007504(n+k) - A007504(n-1).

T(n,0) = A000040(n).

T(n,1) = A001043(n) for n>1.

T(n,2) = A034961(n) for n>1.