login
A335406
First position of n in the sequence of run-lengths of the sequence of prime gaps.
6
1, 2, 49, 633353, 6706139
OFFSET
1,2
COMMENTS
Prime gaps are differences between adjacent prime numbers.
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.
Sequence in context: A088067 A145676 A366672 * A291188 A225795 A027619
KEYWORD
nonn,more,hard
AUTHOR
Gus Wiseman, Jun 10 2020
EXTENSIONS
a(5) from Giovanni Resta, Jun 11 2020
STATUS
approved