A172112 -id:A172112 - cp's OEIS frontend

A172295 Partial sums of A023201.

5, 12, 23, 36, 53, 76, 107, 144, 185, 232, 285, 346, 413, 486, 569, 666, 767, 870, 977, 1108, 1259, 1416, 1583, 1756, 1947, 2140, 2363, 2590, 2823, 3074, 3331, 3594, 3865, 4142, 4449, 4760, 5091, 5438, 5791, 6158, 6531, 6914, 7347, 7790, 8247

Offset: 1

Jonathan Vos Post, Jan 30 2010

A023201 is also known as the smaller numbers of pairs of sexy primes. The subsequence of prime partial sums of smaller numbers of pairs of sexy primes begins 5, 23, 53, 107, 569, 977, 1259, 1583, 3331. The subsubsequence of smaller numbers of pairs of sexy prime partial sums of smaller numbers of pairs of sexy primes begins 5, 107, 977. This is to smaller members of sexy prime pairs as A172112 is to A023200 smaller member p of cousin prime pairs (p, p+4)

			a(19) = 5 + 7 + 11 + 13 + 17 + 23 + 31 + 37 + 41 + 47 + 53 + 61 + 67 + 73 + 83 + 97 + 101 + 103 + 107 = 977, which is A023201(73).

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

Cf. A000040, A023201, A172112.

Accumulate[Select[Prime[Range[120]],PrimeQ[#+6]&]] (* Harvey P. Dale, Jan 18 2020 *)

More terms from Sean A. Irvine, Sep 27 2011

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

Original entry on oeis.org

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

Artur Jasinski, Feb 01 2023

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

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

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

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

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

cp's OEIS Frontend

A172295 Partial sums of A023201.

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