cp's OEIS Frontend

A354233 Least number with n runs in ordered prime signature.

%I A354233 #6 May 21 2022 19:40:16
%S A354233 1,2,12,90,2100,48510,3303300,139369230,18138420300,1157182716690,
%T A354233 278261505822300,30168910606824990,9894144362523521100,
%U A354233 1693350783450479863710,715178436956287675671300,147157263134197051595990130,83730945863531292204568790100
%N A354233 Least number with n runs in ordered prime signature.
%C A354233 A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.
%H A354233 Mathematics Stack Exchange, <a href="https://math.stackexchange.com/q/87559">What is a sequence run? (answered 2011-12-01)</a>
%e A354233 The prime indices of 90 are {1,2,2,3}, with multiplicities {1,2,1}, with runs {{1},{2},{1}}, and this is the first case of 3 runs, so a(3) = 90.
%t A354233 Table[Product[Prime[i]^If[EvenQ[n-i],1,2],{i,n}],{n,0,15}]
%Y A354233 Positions of first appearances in A353745.
%Y A354233 A001222 counts prime factors with multiplicity, distinct A001221.
%Y A354233 A005361 gives product of signature, firsts A353500 (sorted A085629).
%Y A354233 A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A354233 A124010 gives prime signature, sorted A118914.
%Y A354233 A130091 lists numbers with distinct prime exponents, counted by A098859.
%Y A354233 A181819 gives prime shadow, with an inverse A181821.
%Y A354233 A182850 gives frequency depth of prime indices, counted by A225485.
%Y A354233 A323014 gives adjusted frequency depth of prime indices, counted by A325280.
%Y A354233 Cf. A005811, A097318, A304678, A325755, A353507, A353742.
%K A354233 nonn
%O A354233 0,2
%A A354233 _Gus Wiseman_, May 20 2022