OFFSET
1,1
COMMENTS
First differs from A335448 in having 270.
A sequence is alternating if it is alternately strictly increasing and strictly decreasing, starting with either. For example, the partition (3,2,2,2,1) has no alternating permutations, even though it has the anti-run permutations (2,3,2,1,2) and (2,1,2,3,2).
Also Heinz numbers of integer partitions without a wiggly permutation, where the Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
EXAMPLE
The sequence of terms together with their prime indices begins:
4: {1,1}
8: {1,1,1}
9: {2,2}
16: {1,1,1,1}
24: {1,1,1,2}
25: {3,3}
27: {2,2,2}
32: {1,1,1,1,1}
40: {1,1,1,3}
48: {1,1,1,1,2}
49: {4,4}
54: {1,2,2,2}
56: {1,1,1,4}
64: {1,1,1,1,1,1}
80: {1,1,1,1,3}
81: {2,2,2,2}
88: {1,1,1,5}
96: {1,1,1,1,1,2}
MATHEMATICA
wigQ[y_]:=Or[Length[y]==0, Length[Split[y]]== Length[y]&&Length[Split[Sign[Differences[y]]]]==Length[y]-1];
Select[Range[100], Select[Permutations[Flatten[ ConstantArray@@@FactorInteger[#]]], wigQ]=={}&]
CROSSREFS
Positions of 0's in A345164.
The partitions with these Heinz numbers are counted by A345165.
A344606 counts alternating permutations of prime indices with twins.
A344742 ranks twins and partitions with an alternating permutation.
A345192 counts non-alternating compositions.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 13 2021
STATUS
approved