A014148 a(n) = Sum_{m=1..n} Sum_{k=1..m} prime(k).

2, 7, 17, 34, 62, 103, 161, 238, 338, 467, 627, 824, 1062, 1343, 1671, 2052, 2492, 2993, 3561, 4200, 4912, 5703, 6577, 7540, 8600, 9761, 11025, 12396, 13876, 15469, 17189, 19040, 21028, 23155, 25431, 27858, 30442, 33189, 36103, 39190, 42456, 45903

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Previous name was: Apply partial sum operator twice to sequence of primes.

Numbers n such that a(n) is prime are listed in A122381(n) = {1, 2, 3, 6, 10, 23, 31, 46, 55, 58, 66, 70, 82, 91, 118, 131, 151, 163, 182, 187, 198, 199, ...}. Corresponding primes a(n) = a( A122381(n) ) = A122382(n) = {2, 7, 17, 103, 467, 6577, 17189, 61627, 109919, 130531, 198109, 239579, 399557, 559313, ...}. - Alexander Adamchuk, Aug 30 2006

Row 2 in A254858. - Reinhard Zumkeller, Feb 08 2015

Partial sums of A007504, n>=1. - Omar E. Pol, Nov 23 2016

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000 [extending prior b-File from Alexander Adamchuk]

Crossrefs

Cf. A000040, A007504, A014150, A122381, A122382, A178138, A254784, A254858.

Programs

Haskell

a014148 n = a014148_list !! (n-1)
a014148_list = (iterate (scanl1 (+)) a000040_list) !! 2
-- Reinhard Zumkeller, Feb 08 2015

Maple

b:= proc(n) option remember; `if`(n<1, [0$2],
      (p-> p+[ithprime(n), p[1]])(b(n-1)))
    end:
a:= n-> b(n+1)[2]:
seq(a(n), n=1..42);  # Alois P. Heinz, Oct 07 2021

Mathematica

Table[Sum[Sum[Prime[k],{k,1,m}],{m,1,n}],{n,1,100}] (* Alexander Adamchuk, Aug 30 2006 *)
Accumulate[Accumulate[Prime[Range[50]]]] (* Harvey P. Dale, Dec 29 2011 *)

Formula

Convolution of the primes with the positive integers: Sum_{k=1..n} (n-k+1)*prime(k). - David Scambler, Oct 08 2006

Extensions

More terms from Alexander Adamchuk, Aug 30 2006

Name changed by Wesley Ivan Hurt, Oct 04 2021