A370372 Row lengths of A369276.
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, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
Offset: 1
Examples
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.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
1 + Map[Length, SplitBy[Differences@ Select[Range[1000], Nor[PrimePowerQ[#], SquareFreeQ[#]] &], # == 1 &]][[2 ;; -1 ;; 2]]
Comments