A345314 Primes that can be constructed by concatenating two squares >= 4.

449, 499, 1009, 1699, 2549, 4289, 4441, 4729, 6449, 6481, 8419, 9619, 12149, 14449, 16361, 16529, 16729, 16981, 19681, 21169, 22549, 24019, 25121, 25169, 25841, 28099, 28949, 30259, 34819, 36529, 38449, 41521, 41681, 41849, 42209, 43481, 43721, 43969, 45329, 46889

Offset: 1

Author

Tanya Khovanova, Jun 13 2021

Keywords

• nonn
• base

Comments

If we allow 1, we get sequence A167535.

Examples

			449 is a prime that is a concatenation of two squares: 4 and 49.
		

Links

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

Crossrefs

Cf. A167535.

Programs

Maple

zcat:= proc(a,b) 10^(1+ilog10(b))*a+b end proc:
select(t -> t <= 10^5 and isprime(t), {seq(seq(zcat(a^2,b^2),a=2..100),b=3..1000,2)}); # Robert Israel, Jun 17 2021

Mathematica

Take[Select[Union[Flatten[Table[FromDigits[Join[IntegerDigits[n^2],IntegerDigits[k^2]]], {n, 2, 300}, {k, 2, 300}]]], PrimeQ[#] &], 60]

Python

from sympy import isprime
def aupto(lim):
  s = list(i**2 for i in range(2, int(lim**(1/2))+2))
  t = set(int(str(a)+str(b)) for a in s for b in s)
  return sorted(filter(isprime, filter(lambda x: x<=lim, t)))
print(aupto(49000)) # Michael S. Branicky, Jun 13 2021