A356223 Position of n-th appearance of 2n in the sequence of prime gaps (A001223). If 2n does not appear at least n times, set a(n) = -1.

2, 6, 15, 79, 68, 121, 162, 445, 416, 971, 836, 987, 2888, 1891, 1650, 5637, 5518, 4834, 9237, 8152, 10045, 21550, 20248, 20179, 29914, 36070, 24237, 53355, 52873, 34206, 103134, 90190, 63755, 147861, 98103, 117467, 209102, 206423, 124954, 237847, 369223

Offset: 1

Author

Gus Wiseman, Aug 04 2022

Keywords

• nonn

Comments

Prime gaps (A001223) are the differences between consecutive prime numbers. They begin: 1, 2, 2, 4, 2, 4, 2, 4, 6, ...

Examples

			We need the first 15 prime gaps (1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6) before we reach the 3rd appearance of 6, so a(6) = 15.
		

Crossrefs

The first appearances are at A038664, seconds A356221.

Diagonal of A356222.

A001223 lists the prime gaps.

A073491 lists numbers with gapless prime indices.

A356224 counts divisors with gapless prime indices, complement A356225.

A356226 = gapless interval lengths of prime indices, run-lengths A287170.

Cf. A000005, A028334, A029709, A060681, A119313, A137921, A193829, A274121.

Programs

Mathematica

nn=1000;
gaps=Differences[Array[Prime,nn]];
Table[Position[gaps,2*n][[n,1]],{n,Select[Range[nn],Length[Position[gaps,2*#]]>=#&]}]