cp's OEIS Frontend

A351925 Squares which are the concatenation of two primes.

%I A351925 #21 Oct 08 2023 09:29:35
%S A351925 25,289,361,529,729,2401,2601,2809,4761,5329,5929,7569,11449,11881,
%T A351925 15129,19881,21609,22801,23409,24649,25281,26569,29241,29929,31329,
%U A351925 34969,36481,39601,47961,52441,53361,54289,57121,58081,59049,71289,77841,83521,89401
%N A351925 Squares which are the concatenation of two primes.
%C A351925 The first term that is the concatenation of two primes in more than one way is a(11) = 5929 = 5 | 929 = 59 | 29. - _Robert Israel_, Oct 01 2023
%H A351925 Robert Israel, <a href="/A351925/b351925.txt">Table of n, a(n) for n = 1..10000</a>
%F A351925 Intersection of A106582 and A000290.
%e A351925 25 is the concatenation of 2 and 5, both primes.
%e A351925 4761 is the concatenation of 47 and 61, both primes.
%p A351925 L:= NULL: count:=0:
%p A351925 for x from 1 by 2 while count < 100 do
%p A351925   xs:= x^2;
%p A351925   for i from 1 to ilog10(xs) do
%p A351925     a:= xs mod 10^i;
%p A351925     if a > 10^(i-1) and isprime(a) then
%p A351925       b:= (xs-a)/10^i;
%p A351925       if isprime(b) then
%p A351925         L:= L, xs; count:= count+1; break
%p A351925       fi fi
%p A351925 od od:
%p A351925 L; # _Robert Israel_, Oct 01 2023
%o A351925 (PARI)
%o A351925 isb(n)={my(d=10); while(d<n, if(isprime(n%d)&&isprime(n\d), return(1)); d*=10); 0}
%o A351925 { for(n=1, 300, if(isb(n^2), print1(n^2, ", ")))} \\ _Andrew Howroyd_, Feb 26 2022
%o A351925 (Python)
%o A351925 from sympy import isprime
%o A351925 from itertools import count, islice
%o A351925 def agen(): # generator of terms
%o A351925     for k in count(1):
%o A351925         s = str(k*k)
%o A351925         if any(s[i] != '0' and isprime(int(s[:i])) and isprime(int(s[i:])) for i in range(1, len(s))):
%o A351925             yield k*k
%o A351925 print(list(islice(agen(), 39))) # _Michael S. Branicky_, Feb 26 2022
%Y A351925 Cf. A000290 (squares), A039686, A106582, inverse of A167535.
%Y A351925 Cf. A038692, A225135.
%K A351925 nonn,base
%O A351925 1,1
%A A351925 _Max Z. Scialabba_, Feb 25 2022