cp's OEIS Frontend

A382775 Least number appearing n times in A048767 (rank of Look-and-Say partition of prime indices).

%I A382775 #6 Apr 13 2025 21:08:57
%S A382775 6,1,8,32,64,128,256,6144,512,27648,1024,73728,2048,147456,165888,
%T A382775 4096,248832,196608,8192,497664,1119744,393216,16384,2239488
%N A382775 Least number appearing n times in A048767 (rank of Look-and-Say partition of prime indices).
%C A382775 Also the position of first appearance of n in A382525 (number of times n appears in A048767).
%C A382775 The Look-and-Say partition of a multiset or partition y is obtained by interchanging parts with multiplicities. Hence, the multiplicity of k in the Look-and-Say partition of y is the sum of all parts that appear exactly k times. For example, starting with (3,2,2,1,1) we get (2,2,2,1,1,1), the multiset union of ((1,1,1),(2,2),(2)).
%C A382775 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, sum A056239.
%e A382775 The terms together with their prime indices begin:
%e A382775        6: {1,2}
%e A382775        1: {}
%e A382775        8: {1,1,1}
%e A382775       32: {1,1,1,1,1}
%e A382775       64: {1,1,1,1,1,1}
%e A382775      128: {1,1,1,1,1,1,1}
%e A382775      256: {1,1,1,1,1,1,1,1}
%e A382775     6144: {1,1,1,1,1,1,1,1,1,1,1,2}
%e A382775      512: {1,1,1,1,1,1,1,1,1}
%e A382775    27648: {1,1,1,1,1,1,1,1,1,1,2,2,2}
%e A382775     1024: {1,1,1,1,1,1,1,1,1,1}
%e A382775    73728: {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2}
%e A382775     2048: {1,1,1,1,1,1,1,1,1,1,1}
%e A382775   147456: {1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2}
%e A382775   165888: {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2}
%e A382775     4096: {1,1,1,1,1,1,1,1,1,1,1,1}
%e A382775   248832: {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2}
%t A382775 stp[y_]:=Select[Tuples[Select[IntegerPartitions[#], UnsameQ@@#&]&/@y],UnsameQ@@Join@@#&];
%t A382775 z=Table[Length[stp[Last/@FactorInteger[n]]],{n,10000}];
%t A382775 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A382775 Table[Position[z,k][[1,1]],{k,0,mnrm[z+1]-1}]
%Y A382775 Positions of first appearances in A382525.
%Y A382775 The Look-and-Say partition is ranked by A048767, listed by A381440.
%Y A382775 Look-and-Say partitions are counted by A239455, complement A351293.
%Y A382775 Look-and-Say partitions are ranked by A351294.
%Y A382775 Non-Look-and-Say partitions are ranked by A351295, conjugate A381433.
%Y A382775 The section-sum partition is ranked by A381431, listed by A381436.
%Y A382775 Section-sum partitions are ranked by A381432.
%Y A382775 A055396 gives least prime index, greatest A061395.
%Y A382775 A056239 adds up prime indices, row sums of A112798.
%Y A382775 A122111 represents conjugation in terms of Heinz numbers.
%Y A382775 Cf. A003557, A047966, A048768, A051903, A051904, A066328, A071178, A116861, A130091, A217605, A239964, A381540.
%K A382775 nonn,more
%O A382775 0,1
%A A382775 _Gus Wiseman_, Apr 11 2025