A382772 Set of positions of first appearances in A382771 (permutations of prime indices with distinct run-lengths).

1, 6, 12, 96, 360, 1536, 3456, 5184, 5760, 6144, 7776, 13824, 23040, 24576, 55296, 62208, 92160

Offset: 1

Author

Gus Wiseman, Apr 09 2025

Keywords

• nonn
• more

Examples

			The permutations for n = 12, 96, 360, 1536:
  (1,1,2)  (1,1,1,1,1,2)  (1,1,1,2,2,3)  (1,1,1,1,1,1,1,1,1,2)
  (2,1,1)  (1,1,1,2,1,1)  (1,1,1,3,2,2)  (1,1,1,1,1,1,1,2,1,1)
           (1,1,2,1,1,1)  (2,2,1,1,1,3)  (1,1,1,1,1,1,2,1,1,1)
           (2,1,1,1,1,1)  (2,2,3,1,1,1)  (1,1,1,1,1,2,1,1,1,1)
                          (3,1,1,1,2,2)  (1,1,1,1,2,1,1,1,1,1)
                          (3,2,2,1,1,1)  (1,1,1,2,1,1,1,1,1,1)
                                         (1,1,2,1,1,1,1,1,1,1)
                                         (2,1,1,1,1,1,1,1,1,1)
		

Crossrefs

Positions of first appearances in A382771, by signature A382773.

For equal run-lengths we have A382878, firsts of A382857, zeros A382879.

A044813 lists numbers whose binary expansion has distinct run-lengths, equal A140690.

A055396 gives least prime index, greatest A061395.

A056239 adds up prime indices, row sums of A112798.

A098859 counts partitions with distinct multiplicities, ordered A242882.

A239455 counts Look-and-Say partitions, ranks A351294, conjugate A381432.

A328592 lists numbers whose binary form has distinct runs of ones, equal A164707.

A329738 counts compositions with equal run-lengths, ranks A353744.

A329739 counts compositions with distinct run-lengths, ranks A351596.

A351293 counts non-Look-and-Say partitions, ranks A351295, conjugate A381433.

Cf. A000720, A001221, A001222, A003242, A048767, A130091, A238130, A305936, A351013, A351202, A382876.

Programs

Mathematica

y=Table[Length[Select[Permutations[Join@@ConstantArray@@@FactorInteger[n]],UnsameQ@@Length/@Split[#]&]],{n,0,100000}];
fip[y_]:=Select[Range[Length[y]],!MemberQ[Take[y,#-1],y[[#]]]&];
fip[Rest[y]]