A048646 Primes p such that the decimal digits of p^2 can be partitioned into two or more nonzero squares.

7, 13, 19, 37, 41, 107, 191, 223, 379, 487, 997, 1063, 1093, 1201, 1301, 1907, 2029, 3019, 3169, 3371, 5081, 5099, 5693, 6037, 9041, 9619, 9721, 9907, 10007, 11681, 12227, 12763, 17393, 18493, 19013, 19213, 19219, 21059, 21157, 21193, 25931

Offset: 1

Author

Felice Russo

Keywords

• nice
• nonn
• base

Examples

			7 is present because 7^2=49 can be partitioned into two squares 4 and 9; 13^2 = 169 = 16_9; 37^2 = 1369 = 1_36_9.
997^2 = 994009 = 9_9_400_9, 1063^2 = 1129969 = 1_12996_9, 997 and 1063 are primes, so 997 and 1063 are in the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A048375.

Cf. A010051, intersection of A048653 and A000040.

Programs

Haskell

a048646 n = a048646_list !! (n-1)
a048646_list = filter ((== 1) . a010051') a048653_list
-- Reinhard Zumkeller, Apr 17 2015

Python

from math import isqrt
from sympy import primerange
def issquare(n): return isqrt(n)**2 == n
def ok(n, c):
    if n%10 in {2, 3, 7, 8}: return False
    if issquare(n) and c > 1: return True
    d = str(n)
    for i in range(1, len(d)):
        if d[i] != '0' and issquare(int(d[:i])) and ok(int(d[i:]), c+1):
            return True
    return False
def aupto(lim): return [p for p in primerange(1, lim+1) if ok(p*p, 1)]
print(aupto(25931)) # Michael S. Branicky, Jul 10 2021

Extensions

Corrected and extended by Naohiro Nomoto, Sep 01 2001

"Nonzero" added to definition by N. J. A. Sloane, May 08 2021