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 A014148 Apply partial sum operator twice to sequence of primes. 14
 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: A045947 A321123 A145066 * A070070 A318054 A033937 Adjacent sequences:  A014145 A014146 A014147 * A014149 A014150 A014151 KEYWORD nonn AUTHOR EXTENSIONS More terms from Alexander Adamchuk, Aug 30 2006 STATUS approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)