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A384235 a(n) is the least number that is the concatenation of n consecutive primes, in increasing order, and is the product of n primes, counted with multiplicity.

%I A384235 #17 Jun 03 2025 02:28:06
%S A384235 2,35,357,11131719,3571113,5711131719,463467479487491499503,
%T A384235 811821823827829839853857,103910491051106110631069108710911093,
%U A384235 1291129713011303130713191321132713611367,19011907191319311933194919511973197919871993,109091093710939109491095710973109791098710993110031102711047
%N A384235 a(n) is the least number that is the concatenation of n consecutive primes, in increasing order, and is the product of n primes, counted with multiplicity.
%e A384235 a(4) = 11131719 is the concatenation of four consecutive primes 11, 13, 17, 19, and 11131719 = 3 * 17 * 167 * 1307 is the product of four primes.
%p A384235 lcat:= proc(L) local r,i;
%p A384235    r:= L[1];
%p A384235    for i from 2 to nops(L) do
%p A384235      r:= r * 10^(1+ilog10(L[i]))+L[i]
%p A384235    od;
%p A384235    r
%p A384235 end proc:
%p A384235 f:= proc(n) local i,j,x;
%p A384235      for i from 1 do
%p A384235        x:= lcat([seq(ithprime(j),j=i..i+n-1)]);
%p A384235        if numtheory:-bigomega(x) = n then return x fi
%p A384235      od;
%p A384235 end proc:
%p A384235 map(f, [$1..13]);
%t A384235 a[n_]:=Module[{i=1},While[PrimeOmega[m={};Do[m=Join[m,IntegerDigits[Prime[j]]],{j,i,i+n-1}];ln=FromDigits[m]]!=n,i++];ln];Array[a,11] (* _James C. McMahon_, Jun 02 2025 *)
%Y A384235 Cf. A383114.
%K A384235 nonn,base
%O A384235 1,1
%A A384235 _Robert Israel_, May 23 2025