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A048646 Primes p such that the decimal digits of p^2 can be partitioned into two or more nonzero squares. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

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.

PROG

(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

CROSSREFS

Cf. A048375.

Cf. A010051, intersection of A048653 and A000040.

Sequence in context: A108295 A071923 A344045 * A152087 A098059 A078860

Adjacent sequences:  A048643 A048644 A048645 * A048647 A048648 A048649

KEYWORD

nice,nonn,base

AUTHOR

Felice Russo

EXTENSIONS

Corrected and extended by Naohiro Nomoto, Sep 01 2001

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

STATUS

approved

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Last modified May 20 11:16 EDT 2022. Contains 353871 sequences. (Running on oeis4.)