OFFSET
1,1
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]
FORMULA
Convolution of the primes with the positive integers: Sum_{k=1..n} (n-k+1)*prime(k). - David Scambler, Oct 08 2006
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 *)
PROG
(Haskell)
a014148 n = a014148_list !! (n-1)
a014148_list = (iterate (scanl1 (+)) a000040_list) !! 2
-- Reinhard Zumkeller, Feb 08 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Alexander Adamchuk, Aug 30 2006
Name changed by Wesley Ivan Hurt, Oct 04 2021
STATUS
approved