A395338 Primes whose square is a concatenation of exactly 2 distinct nonzero squares.

7, 13, 19, 41, 223, 487, 1201, 1301, 18493, 32009, 110237, 282001, 1039681, 2380531, 96799849, 1012639687, 4999900001, 19976430247, 20544050201, 109860000049

Offset

1,1

Comments

Also, primes in A048375.

Conjecture: sequence is infinite.

Contains 10^(2*k)/2 - 10^k + 1 for k in A296445. - Robert Israel, Apr 29 2026

Also contains all primes p > 3 in A228209: their square is the concatenation of the squares of floor(p^2/10) and 3. For example, 55450123962253 is also a term. - M. F. Hasler, Apr 30 2026

Links

Table of n, a(n) for n=1..20.

Example

The following primes squared are concatenation of distinct squares and therefore in the sequence:
7^2 = 49 = concat(2^2, 3^2).
13^2 = 169 = concat(4^2, 3^2).
19^2 = 361 = concat(6^2, 1^2).
...
Numbers 10^(2*k)/2 - 10^k + 1 with k in A296445 are primes, and their square is the concatenation of (10^k/2-1)^2 and (10^k-1)^2. - M. F. Hasler, Apr 30 2026

Prog

(PARI) is_A395338(p, i=isprime(p))=my(s=p^2, t=1); i&&while(s>t*=10, r=divrem(s, t); r[2]*10>=t && issquare(r[1])&&issquare(r[2])&&r[1]!=r[2]&&return(1))
forprime(p=1, , is_A395338(p, 1) && print1(p", ")) \\ M. F. Hasler, Apr 30 2026

Crossrefs

Primes in A048375.

Cf. A000290, A066591, A106497, A048375, A039686, A296445.

Sequence in context: A058383 A005471 A249381 * A040096 A358322 A181938

Adjacent sequences: A395335 A395336 A395337 * A395339 A395340 A395341

Keyword

nonn,base,more

Author

Pang Ern, Apr 19 2026

Status

approved