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A014148
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Apply partial sum operator twice to sequence of primes.
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8
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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; internal format)
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OFFSET
| 1,1
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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 (alex(AT)kolmogorov.com), Aug 30 2006
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 1..10000 [extending prior b-File from Alexander Adamchuk]
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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 J. Scambler (dscambler(AT)bmm.com), Oct 08 2006
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MATHEMATICA
| Table[Sum[Sum[Prime[k], {k, 1, m}], {m, 1, n}], {n, 1, 100}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 30 2006
Accumulate[Accumulate[Prime[Range[50]]]] (* From Harvey P. Dale, Dec 29 2011 *)
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CROSSREFS
| Cf. A000040, A122381, A122382.
Sequence in context: A083723 A045947 A145066 * A070070 A033937 A116576
Adjacent sequences: A014145 A014146 A014147 * A014149 A014150 A014151
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 30 2006
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