A351925 Squares which are the concatenation of two primes.

25, 289, 361, 529, 729, 2401, 2601, 2809, 4761, 5329, 5929, 7569, 11449, 11881, 15129, 19881, 21609, 22801, 23409, 24649, 25281, 26569, 29241, 29929, 31329, 34969, 36481, 39601, 47961, 52441, 53361, 54289, 57121, 58081, 59049, 71289, 77841, 83521, 89401

Offset

1,1

Comments

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

Links

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

Formula

Intersection of A106582 and A000290.

Example

25 is the concatenation of 2 and 5, both primes.
4761 is the concatenation of 47 and 61, both primes.

Maple

L:= NULL: count:=0:
for x from 1 by 2 while count < 100 do
  xs:= x^2;
  for i from 1 to ilog10(xs) do
    a:= xs mod 10^i;
    if a > 10^(i-1) and isprime(a) then
      b:= (xs-a)/10^i;
      if isprime(b) then
        L:= L, xs; count:= count+1; break
      fi fi
od od:
L; # Robert Israel, Oct 01 2023

Prog

(PARI)
isb(n)={my(d=10); while(d<n, if(isprime(n%d)&&isprime(n\d), return(1)); d*=10); 0}
{ for(n=1, 300, if(isb(n^2), print1(n^2, ", ")))} \\ Andrew Howroyd, Feb 26 2022
(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    for k in count(1):
        s = str(k*k)
        if any(s[i] != '0' and isprime(int(s[:i])) and isprime(int(s[i:])) for i in range(1, len(s))):
            yield k*k
print(list(islice(agen(), 39))) # Michael S. Branicky, Feb 26 2022

Crossrefs

Cf. A000290 (squares), A039686, A106582, inverse of A167535.

Cf. A038692, A225135.

Sequence in context: A160084 A265967 A225873 * A029987 A017582 A335598

Adjacent sequences: A351922 A351923 A351924 * A351926 A351927 A351928

Keyword

nonn,base

Author

Max Z. Scialabba, Feb 25 2022

Status

approved