A360226 a(n) = sum of the first n primes whose distance to next prime is 4.

7, 20, 39, 76, 119, 186, 265, 362, 465, 574, 701, 864, 1057, 1280, 1509, 1786, 2093, 2406, 2755, 3134, 3531, 3970, 4427, 4890, 5377, 5876, 6489, 7132, 7805, 8544, 9301, 10070, 10893, 11746, 12605, 13482, 14365, 15272, 16209, 17176, 18185, 19272, 20365, 21578, 22857, 24154, 25457, 26880, 28309, 29756

Offset: 1

Author

Artur Jasinski, Feb 01 2023

Keywords

• nonn
• easy

Links

• Sidney Cadot, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007504, A029710, A086167, A086168, A172112.

Programs

Mathematica

ii = {}; sum = 0; Do[If[Prime[n + 1] - Prime[n] == 4, sum = sum + Prime[n]; AppendTo[ii, sum]], {n, 1, 250}]; ii

Formula

a(n) = Sum_{k=1..n} A029710(k).

a(n) = A172112(n+1) - 3.