OFFSET
1,1
COMMENTS
An anti-run is a sequence with no adjacent equal terms.
The minima of maximal anti-runs in a sequence are obtained by splitting it into maximal anti-run subsequences and taking the least term of each.
Note the prime factors can alternatively be taken in weakly decreasing order.
LINKS
EXAMPLE
The prime factors of 300 are {2,2,3,5,5}, with maximal anti-runs ((2),(2,3,5),(5)), with minima (2,2,5), so 300 is in the sequence.
The prime factors of 450 are {2,3,3,5,5}, with maximal anti-runs ((2,3),(3,5),(5)), with minima (2,3,5), so 450 is not in the sequence.
The terms together with their prime indices begin:
4: {1,1}
8: {1,1,1}
9: {2,2}
12: {1,1,2}
16: {1,1,1,1}
20: {1,1,3}
24: {1,1,1,2}
25: {3,3}
27: {2,2,2}
28: {1,1,4}
32: {1,1,1,1,1}
36: {1,1,2,2}
40: {1,1,1,3}
44: {1,1,5}
45: {2,2,3}
48: {1,1,1,1,2}
MATHEMATICA
Select[Range[100], !UnsameQ@@Min /@ Split[Flatten[ConstantArray@@@FactorInteger[#]], UnsameQ]&]
CROSSREFS
Partitions (or reversed partitions) of this type are counted by A375404.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 16 2024
STATUS
approved