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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 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.)