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

1,1

Comments

Partial sums of A001043.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = 2sum(prime(i), i = 1 .. n) - (2 + prime(n)). - Alonso del Arte, Apr 21 2016

Example

a(1) = 5 = (2+3).
a(2) = 13 = (2+3) + (3+5).
a(3) = 25 = (2+3) + (3+5) + (5+7).

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 *)

Crossrefs

Cf. A001043, A102725, A102729.

Sequence in context: A064276 A240001 A301685 * A147031 A147220 A269713

Adjacent sequences: A102721 A102722 A102723 * A102725 A102726 A102727

Keyword

easy,nonn

Author

Giovanni Teofilatto, Feb 07 2005

Extensions

Edited and extended by Ray Chandler, Feb 12 2005

Better definition from Alonso del Arte, Apr 26 2016

Status

approved