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%I #40 Sep 08 2022 08:46:24
%S 0,1,2,3,10,20,30,100,200,245,247,249,251,253,283,300,448,548,949,
%T 1000,1249,1253,1416,1747,1749,1751,1753,1755,2000,2245,2247,2249,
%U 2251,2253,2429,2450,2451,2470,2490,2498,2510,2530,2647,2830,3000,3747,3751,4480,4899
%N Nonnegative integers k such that k and k^2 have the same number of nonzero digits.
%C The idea of this sequence comes from the 1st problem of the 28th British Mathematical Olympiad in 1992 (see the link).
%C This sequence is infinite because the family of integers {10^k, k >= 0} (A011557) belongs to this sequence.
%C 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
%D A. Gardiner, The Mathematical Olympiad Handbook: An Introduction to Problem Solving, Oxford University Press, 1997, reprinted 2011, Pb 1 pp. 57 and 109 (1992)
%H Giovanni Resta, <a href="/A328780/b328780.txt">Table of n, a(n) for n = 1..10000</a>.
%H British Mathematical Olympiad, <a href="https://bmos.ukmt.org.uk/home/bmo1-1992.pdf">1992 - Problem 1</a>.
%H <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%e 247^2 = 61009, hence 247 and 61009 both have 3 nonzero digits, 247 is a term.
%p q:= n->(f->f(n)=f(n^2))(t->nops(subs(0=[][], convert(t, base, 10)))):
%p select(q, [$0..5000])[]; # _Alois P. Heinz_, Oct 27 2019
%t Select[Range[0, 5000], Equal @@ Total /@ Sign@ IntegerDigits[{#, #^2}] &] (* _Giovanni Resta_, Feb 27 2020 *)
%o (Magma) nz:=func<n|#Intseq(n)-Multiplicity(Intseq(n),0)>; [k:k in [0..5000] | nz(k) eq nz(k^2)]; // _Marius A. Burtea_, Dec 21 2020
%o (PARI) isok(k) = hammingweight(digits(k)) == hammingweight(digits(k^2)); \\ _Michel Marcus_, Dec 22 2020
%Y Subsequences: A011557, A093136, A093138.
%Y Cf. A052040, A104315, A134844.
%Y Cf. A328781, A328782, A328783.
%K nonn,base
%O 1,3
%A _Bernard Schott_, Oct 27 2019
%E More terms from _Alois P. Heinz_, Oct 27 2019
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