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

1, 2, 49, 633353, 6706139

Offset: 1

Author

Gus Wiseman, Jun 10 2020

Keywords

• nonn
• more
• hard

Comments

Prime gaps are differences between adjacent prime numbers.

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.

Programs

Mathematica

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

Extensions

a(5) from Giovanni Resta, Jun 11 2020