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

1,1

Comments

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

Links

Table of n, a(n) for n=1..41.

Example

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.

Mathematica

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

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.

Sequence in context: A009455 A244443 A346555 * A319336 A007709 A190339

Adjacent sequences: A356220 A356221 A356222 * A356224 A356225 A356226

Keyword

nonn

Author

Gus Wiseman, Aug 04 2022

Status

approved