A068493 Primes which are concatenations of positive squares.

11, 19, 41, 149, 181, 191, 199, 251, 419, 449, 491, 499, 641, 811, 911, 919, 941, 991, 1009, 1181, 1259, 1289, 1361, 1481, 1499, 1619, 1699, 1811, 1949, 1999, 2251, 2549, 2591, 3691, 4001, 4111, 4259, 4289, 4441, 4481, 4649, 4729, 4919, 4999, 6449, 6481, 6491

Offset: 1

Author

Joseph L. Pe, Mar 11 2002

Keywords

• base
• nonn

Examples

			149 is a term of the sequence since it is the concatenation of squares 1, 4, 9.
251 is a term of the sequence since it is the concatenation of squares 25, 1. - _Sean A. Irvine_, Feb 19 2024
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, subsequence of A066591.

Programs

Python

from sympy import primerange
from itertools import count, islice
def iscat(w, A):
    return False if len(w) < 2 else any(w[:i] in A and (w[i:] in A or iscat(w[i:], A)) for i in range(1, len(w)))
def agen():
    S = set()
    for d in count(2):
        S |= {str(i*i) for i in range(10**(d-2), 10**(d-1))}
        for p in primerange(10**(d-1), 10**d):
            if iscat(str(p), S):
                yield p
print(list(islice(agen(), 50))) # Michael S. Branicky, Feb 20 2024

Extensions

Corrected and extended by Sascha Kurz, Mar 26 2002

Data corrected by Sean A. Irvine, Feb 19 2024