A328780 Nonnegative integers k such that k and k^2 have the same number of nonzero digits.

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

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.

Index to sequences related to Olympiads.

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<n|#Intseq(n)-Multiplicity(Intseq(n), 0)>; [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