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A014148 Apply partial sum operator twice to sequence of primes. 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

a(n) = Sum[ Sum[ Prime[k], {k,1,m} ], {m,1,n}].

Convolution of the primes with the positive integers: Sum[ (n-k+1)*Prime[k], {k,1,n} ]. - David Scambler, Oct 08 2006

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

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

Sequence in context: A083723 A045947 A145066 * A070070 A033937 A116576

Adjacent sequences:  A014145 A014146 A014147 * A014149 A014150 A014151

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Alexander Adamchuk, Aug 30 2006

STATUS

approved

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Last modified April 25 00:46 EDT 2017. Contains 285346 sequences.