A102724 Sum of the first n pairs of consecutive primes (for example, a(3) = (2+3) + (3+5) + (5+7) = 25).
5, 13, 25, 43, 67, 97, 133, 175, 227, 287, 355, 433, 517, 607, 707, 819, 939, 1067, 1205, 1349, 1501, 1663, 1835, 2021, 2219, 2423, 2633, 2849, 3071, 3311, 3569, 3837, 4113, 4401, 4701, 5009, 5329, 5659, 5999, 6351, 6711, 7083, 7467, 7857, 8253, 8663, 9097
Offset: 1
Examples
a(1) = 5 = (2+3). a(2) = 13 = (2+3) + (3+5). a(3) = 25 = (2+3) + (3+5) + (5+7).
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
Table[Sum[Prime[i] + Prime[i + 1], {i, n}], {n, 47}] (* Ray Chandler, Feb 12 2005 *) Table[2Sum[Prime[i], {i, n}] - (2 + Prime[n]), {n, 2, 50}] (* Alonso del Arte, Apr 26 2016 *) Accumulate[Total/@Partition[Prime[Range[50]],2,1]] (* Harvey P. Dale, Apr 13 2019 *)
Formula
a(n) = 2*Sum_{i=1..n} prime(i) - (2 + prime(n)). - Alonso del Arte, Apr 21 2016
a(n) = 3*n*(n-1)+7 for n = 2, ..., 8; cf. A378569. - M. F. Hasler, Feb 04 2025
Extensions
Edited and extended by Ray Chandler, Feb 12 2005
Better definition from Alonso del Arte, Apr 26 2016
Comments