A078731 Sum of primes between successive pairs of twin primes.

0, 0, 0, 23, 37, 100, 67, 348, 0, 371, 0, 660, 0, 0, 434, 233, 771, 277, 600, 985, 3810, 0, 1788, 3435, 2208, 1757, 1220, 631, 1300, 13190, 0, 0, 1692, 1740, 16239, 0, 1039, 0, 2156, 6678, 10749, 3745, 1283, 1297, 1307, 11040, 4319, 2930, 0, 23259, 1613, 6584

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

Between the 8th and 9th pairs of twin primes are 4 primes: (71,73) 79 83 89 97 (101,103), therefore a(8) = 79+83+89+97 = 348.

Mathematica

seq[lim_] := Module[{p = Prime[Range[lim]], d, i}, d = Differences[p]; i = Position[d, 2] // Flatten; If[First[#] + 2 >= Last[#], 0, Total[p[[First[#] + 2 ;; Last[#] - 1]]]] & /@ Partition[i, 2, 1]]; seq[300] (* Amiram Eldar, Apr 06 2025 *)

Crossrefs

Cf. A001097, A048614.

Sequence in context: A068016 A338270 A140442 * A133957 A133980 A090312

Adjacent sequences: A078728 A078729 A078730 * A078732 A078733 A078734

Keyword

nonn

Author

Reinhard Zumkeller, Dec 20 2002

Status

approved