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 A328780 Nonnegative integers k such that k and k^2 have the same number of nonzero digits. 4
 0, 1, 2, 3, 10, 20, 30, 100, 200, 245, 247, 249, 251, 253, 283, 300, 448, 548, 949, 1000, 1249, 1253, 1416, 1747, 1749, 1751, 1753, 1755, 2000, 2245, 2247, 2249, 2251, 2253, 2429, 2450, 2451, 2470, 2490, 2498, 2510, 2530, 2647, 2830, 3000, 3747, 3751, 4480, 4899 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The idea of this sequence comes from the 1st problem of the 28th British Mathematical Olympiad in 1992 (see the link). This sequence is infinite because the family of integers {10^k, k >= 0} (A011557) belongs to this sequence. The numbers m, m + 1, m + 2 where m = 49*10^k - 3, or m = 99*10^k - 3, k >= 3 are terms with all nonzero digits. - Marius A. Burtea, Dec 21 2020 REFERENCES A. Gardiner, The Mathematical Olympiad Handbook: An Introduction to Problem Solving, Oxford University Press, 1997, reprinted 2011, Pb 1 pp. 57 and 109 (1992) LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000. British Mathematical Olympiad, 1992 - Problem 1. EXAMPLE 247^2 = 61009, hence 247 and 61009 both have 3 nonzero digits, 247 is a term. MAPLE q:= n->(f->f(n)=f(n^2))(t->nops(subs(0=[][], convert(t, base, 10)))): select(q, [\$0..5000])[]; # Alois P. Heinz, Oct 27 2019 MATHEMATICA Select[Range[0, 5000], Equal @@ Total /@ Sign@ IntegerDigits[{#, #^2}] &] (* Giovanni Resta, Feb 27 2020 *) PROG (Magma) nz:=func; [k:k in [0..5000] | nz(k) eq nz(k^2)]; // Marius A. Burtea, Dec 21 2020 (PARI) isok(k) = hammingweight(digits(k)) == hammingweight(digits(k^2)); \\ Michel Marcus, Dec 22 2020 CROSSREFS Subsequences: A011557, A093136, A093138. Cf. A052040, A104315, A134844. Cf. A328781, A328782, A328783. Sequence in context: A083944 A306106 A165550 * A184261 A095919 A285981 Adjacent sequences: A328777 A328778 A328779 * A328781 A328782 A328783 KEYWORD nonn,base AUTHOR Bernard Schott, Oct 27 2019 EXTENSIONS More terms from Alois P. Heinz, Oct 27 2019 STATUS approved

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Last modified January 29 04:14 EST 2023. Contains 359915 sequences. (Running on oeis4.)