A364369 a(n) is the least prime that is the concatenation of n squares, where the concatenations of the last k of these squares are prime for 2 <= k <= n.

11, 419, 4919, 181919, 1981919, 49936919, 991981919, 9991981919, 16999369225919, 136999369225919, 99361981818199181, 1729936999369225919, 3681225936999369225919, 132481225936999369225919, 99362500576936999369225919, 8199362500576936999369225919

Offset: 2

Author

Robert Israel, Oct 20 2023

Keywords

• nonn
• base

Comments

At most 2 of the n squares are not divisible by 9.

Examples

			a(5) = 181919 because it is the concatenation of five squares 1^2 = 1, 9^2 = 81, 3^2 = 9, 1^2 = 1 and 3^2 = 9, and 19, 919, 81919 and 181919 are all prime, and this is the least number that works.
		

Crossrefs

Cf. A167535, A364359.

Programs

Maple

for d from 1 to 8 do
  m1:= ceil(10^((d-1)/2));
  m2:= floor(sqrt(10^d - 1));
  S[d]:= {seq(i^2, i=m1..m2)};
  if m1::even then m1:= m1+1 fi;
  So[d]:= {seq(i^2, i=m1..m2,2)};
od:
for d from 2 to 9 do P[2,d]:= select(isprime, {seq(seq(seq(10^i*s+t, t=So[i]),s=S[d-i]),i=1..d-1)}) od:
L[2]:= 11:
mm[2]:= 2:
for m from 3 do
   found:= false;
   for d from mm[m-1]+1 to m+7 do
     P[m,d]:= select(isprime, {seq(seq(seq(10^i*s+t, t=P[m-1,i]),s=S[d-i]),i=mm[m-1]..d-1)});
     if P[m,d] <> {} and not found then mm[m]:= d; found:= true: L[m]:= min(P[m,d]) fi;
   od;
   if not found then break fi;
od:
seq(L[i],i=2..m-1);