OFFSET
1,2
COMMENTS
EXAMPLE
The terms together with their prime indices begin:
1: () 20: (3,1,1) 47: (15)
2: (1) 23: (9) 48: (2,1,1,1,1)
3: (2) 24: (2,1,1,1) 49: (4,4)
4: (1,1) 25: (3,3) 50: (3,3,1)
5: (3) 27: (2,2,2) 52: (6,1,1)
7: (4) 28: (4,1,1) 53: (16)
8: (1,1,1) 29: (10) 54: (2,2,2,1)
9: (2,2) 31: (11) 56: (4,1,1,1)
11: (5) 32: (1,1,1,1,1) 59: (17)
12: (2,1,1) 37: (12) 61: (18)
13: (6) 40: (3,1,1,1) 63: (4,2,2)
16: (1,1,1,1) 41: (13) 64: (1,1,1,1,1,1)
17: (7) 43: (14) 67: (19)
18: (2,2,1) 44: (5,1,1) 68: (7,1,1)
19: (8) 45: (3,2,2) 71: (20)
For example, the prime indices of 216 are {1,1,1,2,2,2}, and there are four permutations with distinct run-lengths: (1,1,2,2,2,1), (1,2,2,2,1,1), (2,1,1,1,2,2), (2,2,1,1,1,2); so 216 is in the sequence. It is the Heinz number of the Look-and-Say partition of (3,3,2,1).
MATHEMATICA
Select[Range[100], Select[Permutations[Join@@ ConstantArray@@@FactorInteger[#]], UnsameQ@@Length/@Split[#]&]!={}&]
CROSSREFS
These partitions are counted by A239455.
A032020 = number of binary expansions with distinct run-lengths.
A044813 = numbers whose binary expansion has all distinct run-lengths.
A181819 = Heinz number of prime signature (prime shadow).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 15 2022
STATUS
approved