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.

2, 35, 357, 11131719, 3571113, 5711131719, 463467479487491499503, 811821823827829839853857, 103910491051106110631069108710911093, 1291129713011303130713191321132713611367, 19011907191319311933194919511973197919871993, 109091093710939109491095710973109791098710993110031102711047

Offset: 1

Author

Robert Israel, May 23 2025

Keywords

• nonn
• base

Examples

			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.
		

Crossrefs

Cf. A383114.

Programs

Maple

lcat:= proc(L) local r,i;
   r:= L[1];
   for i from 2 to nops(L) do
     r:= r * 10^(1+ilog10(L[i]))+L[i]
   od;
   r
end proc:
f:= proc(n) local i,j,x;
     for i from 1 do
       x:= lcat([seq(ithprime(j),j=i..i+n-1)]);
       if numtheory:-bigomega(x) = n then return x fi
     od;
end proc:
map(f, [$1..13]);

Mathematica

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 *)