OFFSET
1,1
COMMENTS
Also numbers whose first differences of prime indices do not form an anti-run, meaning there are adjacent equal differences.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
8: {1,1,1} 105: {2,3,4}
16: {1,1,1,1} 108: {1,1,2,2,2}
24: {1,1,1,2} 110: {1,3,5}
27: {2,2,2} 112: {1,1,1,1,4}
30: {1,2,3} 120: {1,1,1,2,3}
32: {1,1,1,1,1} 125: {3,3,3}
40: {1,1,1,3} 128: {1,1,1,1,1,1,1}
48: {1,1,1,1,2} 135: {2,2,2,3}
54: {1,2,2,2} 136: {1,1,1,7}
56: {1,1,1,4} 144: {1,1,1,1,2,2}
60: {1,1,2,3} 150: {1,2,3,3}
64: {1,1,1,1,1,1} 152: {1,1,1,8}
72: {1,1,1,2,2} 160: {1,1,1,1,1,3}
80: {1,1,1,1,3} 162: {1,2,2,2,2}
81: {2,2,2,2} 168: {1,1,1,2,4}
88: {1,1,1,5} 176: {1,1,1,1,5}
96: {1,1,1,1,1,2} 184: {1,1,1,9}
104: {1,1,1,6} 189: {2,2,2,4}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], MatchQ[Differences[primeMS[#]], {___, x_, x_, ___}]&]
CROSSREFS
Anti-run compositions are counted by A003242.
Normal anti-runs of length n + 1 are counted by A005649.
Strict partitions with equal differences are A049980.
Partitions with equal differences are A049988.
These are the Heinz numbers of the partitions *not* counted by A238424.
Permutations avoiding triples in arithmetic progression are A295370.
Strict partitions avoiding triples in arithmetic progression are A332668.
Anti-run compositions are ranked by A333489.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 29 2020
STATUS
approved