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 A258103 Number of pandigital squares (containing each digit exactly once) in base n. 1
 0, 0, 1, 0, 1, 3, 4, 26, 87, 47, 87, 0, 547, 1303, 3402, 0, 24192, 187562 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,6 COMMENTS For n = 18, the smallest and largest pandigital squares are 2200667320658951859841 and 39207739576969100808801. For n = 19, they are 104753558229986901966129 and 1972312183619434816475625. For n = 20, they are 5272187100814113874556176 and 104566626183621314286288961. - Chai Wah Wu, May 20 2015 When n is even, (n-1) is a factor of the pandigital squares.  When n is odd, (n-1)/2 is a factor with the remaining factors being odd.  Therefore, when n is odd and (n-1)/2 has an odd number of 2s as prime factors there are no pandigital squares in base n (e.g. 5, 13, 17 and 21). - Adam J.T. Partridge, May 21 2015 LINKS A. J. T. Partridge, Why there are no pandigital squares in base 13 EXAMPLE For n=4 there is one pandigital square, 3201_4 = 225 = 15^2. For n=6 there is one pandigital square, 452013_6 = 38025 = 195^2. For n=10 there are 87 pandigital squares (A036745). There are no pandigital squares in bases 2, 3, 5 or 13. Hexadecimal has 3402 pandigital squares, the largest is FED5B39A42706C81. PROG (Python) from gmpy2 import isqrt, mpz, digits def A258103(n): # requires 2 <= n <= 62 ....c, sm, sq = 0, mpz(''.join([digits(i, n) for i in range(n-1, -1, -1)]), n), mpz(''.join(['1', '0']+[digits(i, n) for i in range(2, n)]), n) ....m = isqrt(sq) ....sq = m*m ....m = 2*m+1 ....while sq <= sm: ........if len(set(digits(sq, n))) == n: ............c += 1 ........sq += m ........m += 2 ....return c # Chai Wah Wu, May 20 2015 CROSSREFS Cf. A036745, A054038, A071519. Sequence in context: A004206 A302397 A151372 * A300373 A222112 A032832 Adjacent sequences:  A258100 A258101 A258102 * A258104 A258105 A258106 KEYWORD base,nonn,more AUTHOR Adam J.T. Partridge, May 20 2015 EXTENSIONS a(17)-a(19) from Giovanni Resta, May 20 2015 STATUS approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)