cp's OEIS Frontend

A370372 Row lengths of A369276.

%I A370372 #39 Mar 25 2024 21:28:53
%S A370372 2,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,3,2,2,3,2,2,2,2,
%T A370372 2,3,2,2,2,3,2,2,2,2,2,2,2,3,2,2,2,3,2,2,2,2,2,2,5,2,2,2,2,2,2,2,2,2,
%U A370372 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A370372 Row lengths of A369276.
%C A370372 Also 1 more than the number of consecutive 1s in the n-th occasion of a run of 1s in A358089.
%H A370372 Michael De Vlieger, <a href="/A370372/b370372.txt">Table of n, a(n) for n = 1..10000</a>
%e A370372 Define quality Q to signify a number neither squarefree nor prime power. For example, 12 has quality Q but smaller numbers do not.
%e A370372 The smallest number k with quality Q such that either (k-1) or (k+1) (or both) share quality Q is 44.
%e A370372 Since both {44, 45} have quality Q, but 43 and 46 are squarefree, a(1) = 2.
%e A370372 Since both {75, 76} have quality Q, but 74 and 78 are squarefree, a(2) = 2.
%e A370372 Since all of {98, 99, 100} have quality Q but 97 and 101 are prime, a(3) = 3, etc.
%t A370372 1 + Map[Length, SplitBy[Differences@ Select[Range[1000], Nor[PrimePowerQ[#], SquareFreeQ[#]] &], # == 1 &]][[2 ;; -1 ;; 2]]
%Y A370372 Cf. A126706, A369276.
%K A370372 nonn,easy
%O A370372 1,1
%A A370372 _Michael De Vlieger_, Mar 24 2024