cp's OEIS Frontend

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

%I A335406 #9 Jun 12 2020 04:28:38
%S A335406 1,2,49,633353,6706139
%N A335406 First position of n in the sequence of run-lengths of the sequence of prime gaps.
%C A335406 Prime gaps are differences between adjacent prime numbers.
%t A335406 qe=Length/@Split[Differences[Array[Prime,10000]],SameQ];
%t A335406 Table[Position[qe,i][[1,1]],{i,Union[qe]}]
%Y A335406 Positions of first appearances in A333254.
%Y A335406 The unequal version is 7, 1, 4, 15, 10, 36, 5, 6, 84, ...
%Y A335406 The weakly decreasing version is 1, 2, 7, 23, 26, ...
%Y A335406 The weakly increasing version is 5, 2, 3, 1, 81, 193, ...
%Y A335406 The strictly decreasing version is 1, 4, 8, 150, 160, ...
%Y A335406 The strictly increasing version is 6, 1, 4, 38, 221, ...
%Y A335406 Prime gaps are A001223.
%Y A335406 The first term of the first length-n arithmetic progression of consecutive primes is A006560(n), with index A089180(n).
%Y A335406 Positions of adjacent equal prime gaps are A064113.
%Y A335406 Positions of adjacent unequal prime gaps are A333214.
%Y A335406 Cf. A000040, A031217, A054800, A059044, A084758, A090832, A106356, A124767, A238279, A295235, A006560.
%K A335406 nonn,more,hard
%O A335406 1,2
%A A335406 _Gus Wiseman_, Jun 10 2020
%E A335406 a(5) from _Giovanni Resta_, Jun 11 2020