

A014148


Apply partial sum operator twice to sequence of primes.


13



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 bFile 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[ (nk+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 !! (n1)
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: A294866 A045947 A145066 * A070070 A318054 A033937
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



