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A351925 Squares which are the concatenation of two primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A160084 A265967 A225873 * A029987 A017582 A335598
KEYWORD
nonn,base
AUTHOR
Max Z. Scialabba, Feb 25 2022
STATUS
approved

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Last modified June 23 20:17 EDT 2024. Contains 373653 sequences. (Running on oeis4.)