cp's OEIS Frontend

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

%I A382772 #7 Apr 09 2025 23:39:22
%S A382772 1,6,12,96,360,1536,3456,5184,5760,6144,7776,13824,23040,24576,55296,
%T A382772 62208,92160
%N A382772 Set of positions of first appearances in A382771 (permutations of prime indices with distinct run-lengths).
%e A382772 The permutations for n = 12, 96, 360, 1536:
%e A382772   (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)
%e A382772   (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)
%e A382772            (1,1,2,1,1,1)  (2,2,1,1,1,3)  (1,1,1,1,1,1,2,1,1,1)
%e A382772            (2,1,1,1,1,1)  (2,2,3,1,1,1)  (1,1,1,1,1,2,1,1,1,1)
%e A382772                           (3,1,1,1,2,2)  (1,1,1,1,2,1,1,1,1,1)
%e A382772                           (3,2,2,1,1,1)  (1,1,1,2,1,1,1,1,1,1)
%e A382772                                          (1,1,2,1,1,1,1,1,1,1)
%e A382772                                          (2,1,1,1,1,1,1,1,1,1)
%t A382772 y=Table[Length[Select[Permutations[Join@@ConstantArray@@@FactorInteger[n]],UnsameQ@@Length/@Split[#]&]],{n,0,100000}];
%t A382772 fip[y_]:=Select[Range[Length[y]],!MemberQ[Take[y,#-1],y[[#]]]&];
%t A382772 fip[Rest[y]]
%Y A382772 Positions of first appearances in A382771, by signature A382773.
%Y A382772 For equal run-lengths we have A382878, firsts of A382857, zeros A382879.
%Y A382772 A044813 lists numbers whose binary expansion has distinct run-lengths, equal A140690.
%Y A382772 A055396 gives least prime index, greatest A061395.
%Y A382772 A056239 adds up prime indices, row sums of A112798.
%Y A382772 A098859 counts partitions with distinct multiplicities, ordered A242882.
%Y A382772 A239455 counts Look-and-Say partitions, ranks A351294, conjugate A381432.
%Y A382772 A328592 lists numbers whose binary form has distinct runs of ones, equal A164707.
%Y A382772 A329738 counts compositions with equal run-lengths, ranks A353744.
%Y A382772 A329739 counts compositions with distinct run-lengths, ranks A351596.
%Y A382772 A351293 counts non-Look-and-Say partitions, ranks A351295, conjugate A381433.
%Y A382772 Cf. A000720, A001221, A001222, A003242, A048767, A130091, A238130, A305936, A351013, A351202, A382876.
%K A382772 nonn,more
%O A382772 1,2
%A A382772 _Gus Wiseman_, Apr 09 2025