OFFSET
1,1
COMMENTS
Also 1 more than the number of consecutive 1s in the n-th occasion of a run of 1s in A358089.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
EXAMPLE
Define quality Q to signify a number neither squarefree nor prime power. For example, 12 has quality Q but smaller numbers do not.
The smallest number k with quality Q such that either (k-1) or (k+1) (or both) share quality Q is 44.
Since both {44, 45} have quality Q, but 43 and 46 are squarefree, a(1) = 2.
Since both {75, 76} have quality Q, but 74 and 78 are squarefree, a(2) = 2.
Since all of {98, 99, 100} have quality Q but 97 and 101 are prime, a(3) = 3, etc.
MATHEMATICA
1 + Map[Length, SplitBy[Differences@ Select[Range[1000], Nor[PrimePowerQ[#], SquareFreeQ[#]] &], # == 1 &]][[2 ;; -1 ;; 2]]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Mar 24 2024
STATUS
approved