A093974 -id:A093974 - cp's OEIS frontend

A093973 Number of prime pairs below 10^n having a difference of 38.

0, 0, 0, 0, 19, 330, 4498, 51756, 548746, 5517814, 54024702, 520188423, 4957098874, 46933220241, 442604975423, 4164551600019, 39140839016528, 367734226199966

Offset: 1

Enoch Haga, Apr 24 2004

			a(5) = 19 because there are 19 prime gaps of 38 below 10^5.

Siegfried "Zig" Herzog, Frequency of Occurrence of Prime Gaps
T. Oliveira e Silva, S. Herzog, and S. Pardi, Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4.10^18, Math. Comp., 83 (2014), 2033-2060.

Cf. A007508, A093972, A093974.

a(10)-a(13) from Washington Bomfim, Jun 22 2012

a(14)-a(18) from S. Herzog's website added by Giovanni Resta, Aug 14 2018

A093975 Number of prime pairs below 10^n having a difference of 42.

Original entry on oeis.org

0, 0, 0, 0, 19, 476, 7180, 86637, 954456, 9919519, 99655858, 979052296, 9484975460, 91050561862, 868774394325, 8257228721817, 78288453457352, 741199448968875

Offset: 1

Enoch Haga, Apr 24 2004

			a(6) = 476 because there are 476 prime gaps of 42 below 10^6.

Siegfried "Zig" Herzog, Frequency of Occurrence of Prime Gaps
T. Oliveira e Silva, S. Herzog, and S. Pardi, Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4.10^18, Math. Comp., 83 (2014), 2033-2060.

Cf. A007508, A093974, A093976.

Table[Count[Differences[Prime[Range[PrimePi[10^n]]]],42],{n,10}] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Jun 11 2025 *)

a(10)-a(13) from Washington Bomfim, Jun 22 2012

a(14)-a(18) from S. Herzog's website added by Giovanni Resta, Aug 14 2018

cp's OEIS Frontend

A093973 Number of prime pairs below 10^n having a difference of 38.

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