A335406 First position of n in the sequence of run-lengths of the sequence of prime gaps.

1, 2, 49, 633353, 6706139

Offset

1,2

Comments

Prime gaps are differences between adjacent prime numbers.

Links

Table of n, a(n) for n=1..5.

Mathematica

qe=Length/@Split[Differences[Array[Prime, 10000]], SameQ];
Table[Position[qe, i][[1, 1]], {i, Union[qe]}]

Crossrefs

Positions of first appearances in A333254.

The unequal version is 7, 1, 4, 15, 10, 36, 5, 6, 84, ...

The weakly decreasing version is 1, 2, 7, 23, 26, ...

The weakly increasing version is 5, 2, 3, 1, 81, 193, ...

The strictly decreasing version is 1, 4, 8, 150, 160, ...

The strictly increasing version is 6, 1, 4, 38, 221, ...

Prime gaps are A001223.

The first term of the first length-n arithmetic progression of consecutive primes is A006560(n), with index A089180(n).

Positions of adjacent equal prime gaps are A064113.

Positions of adjacent unequal prime gaps are A333214.

Cf. A000040, A031217, A054800, A059044, A084758, A090832, A106356, A124767, A238279, A295235, A006560.

Sequence in context: A088067 A145676 A366672 * A291188 A225795 A027619

Adjacent sequences: A335403 A335404 A335405 * A335407 A335408 A335409

Keyword

nonn,more,hard

Author

Gus Wiseman, Jun 10 2020

Extensions

a(5) from Giovanni Resta, Jun 11 2020

Status

approved