A096279 Sums of successive sums of successive sums of successive sums of successive primes.

83, 122, 168, 216, 264, 316, 378, 446, 514, 582, 644, 700, 766, 846, 924, 994, 1062, 1126, 1188, 1258, 1340, 1434, 1528, 1602, 1656, 1704, 1764, 1860, 1984, 2094, 2178, 2260, 2348, 2432, 2514, 2598, 2682, 2766, 2848, 2932, 3018, 3090, 3152, 3242, 3378

Offset: 1

Author

Cino Hilliard, Jun 22 2004

Keywords

• easy
• nonn

Comments

The first term is always odd and may be prime. The first terms of more and more successions produce A007443.

Examples

			2 3 5 7 11 successive primes
5 8 12 18 sums of successive primes
13 20 30 sums of successive sums of successive primes
33 50 sums of successive sums of successive sums of successive primes
83 sums of successive sums of successive sums of successive sums of successive primes
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001043, A096277, A096278.

Programs

Mathematica

Nest[ListConvolve[{1,1},#]&,Prime[Range[100]],4] (* Paolo Xausa, Oct 31 2023 *)

PARI

\\ Iterated successive sums of successive sums... of successive primes.
\\ Input number of terms n and the order m. m=0 yields the primes.
sucsums(n, m) = { my(a, b, i, j, k); a = primes(n+m); b = vector(#a); for(i=1, m, for(j=1, n+m-i, b[j] = a[j]+ a[j+1]; ); a=b; ); for(k=1, n, print1(a[k], ", "); ) }