cp's OEIS Frontend

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

%I A345314 #16 Jun 18 2021 01:14:30
%S A345314 449,499,1009,1699,2549,4289,4441,4729,6449,6481,8419,9619,12149,
%T A345314 14449,16361,16529,16729,16981,19681,21169,22549,24019,25121,25169,
%U A345314 25841,28099,28949,30259,34819,36529,38449,41521,41681,41849,42209,43481,43721,43969,45329,46889
%N A345314 Primes that can be constructed by concatenating two squares >= 4.
%C A345314 If we allow 1, we get sequence A167535.
%H A345314 Robert Israel, <a href="/A345314/b345314.txt">Table of n, a(n) for n = 1..10000</a>
%e A345314 449 is a prime that is a concatenation of two squares: 4 and 49.
%p A345314 zcat:= proc(a,b) 10^(1+ilog10(b))*a+b end proc:
%p A345314 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
%t A345314 Take[Select[Union[Flatten[Table[FromDigits[Join[IntegerDigits[n^2],IntegerDigits[k^2]]], {n, 2, 300}, {k, 2, 300}]]], PrimeQ[#] &], 60]
%o A345314 (Python)
%o A345314 from sympy import isprime
%o A345314 def aupto(lim):
%o A345314   s = list(i**2 for i in range(2, int(lim**(1/2))+2))
%o A345314   t = set(int(str(a)+str(b)) for a in s for b in s)
%o A345314   return sorted(filter(isprime, filter(lambda x: x<=lim, t)))
%o A345314 print(aupto(49000)) # _Michael S. Branicky_, Jun 13 2021
%Y A345314 Cf. A167535.
%K A345314 nonn,base
%O A345314 1,1
%A A345314 _Tanya Khovanova_, Jun 13 2021