A364359 Primes that are the concatenation of a square and a prime that is the concatenation of two squares.

419, 911, 919, 941, 1181, 1499, 1619, 1811, 4919, 8111, 9181, 9491, 9811, 11699, 12119, 12251, 14411, 14419, 16481, 16811, 19001, 22511, 22541, 32411, 32441, 36251, 44111, 44119, 44729, 49499, 49811, 52919, 57641, 64499, 64811, 67619, 72911, 81181, 90011, 90019, 91009, 92251, 94441, 97841, 98419

Offset: 1

Author

Robert Israel, Oct 20 2023

Keywords

• nonn
• base

Comments

Primes that are the concatenation of a square and a member of A167535.

Examples

			a(5) = 1181 is a term because it is the concatenation of 1^2 = 1, 1^2 =1 and 9^2 = 81, and 181 and 1181 are primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A167535.

Programs

Maple

for d from 1 to 3 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 4 do P2[d]:= select(isprime, {seq(seq(seq(10^i*s+t, t=So[i]),s=S[d-i]),i=1..d-1)}) od:
for d from 3 to 5 do P3[d]:= select(isprime, {seq(seq(seq(10^i*s+t, t=P2[i]),s=S[d-i]),i=2..d-1)}) od:
sort([seq](op(P3[d]),d=3..5));