A278937 Numbers k such that 3 is the largest decimal digit of k^3.

11, 101, 110, 1001, 1010, 1100, 10001, 10010, 10100, 11000, 100001, 100010, 100100, 101000, 110000, 684917, 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 6849170, 10000001, 10000010, 10000100, 10001000, 10010000, 10100000, 11000000

Offset: 1

Author

Colin Barker, Dec 02 2016

Keywords

• nonn
• base

Comments

A038444 is a subsequence. Are there an infinite number of terms not in A038444 that are not a multiple of 10? - Chai Wah Wu, Dec 02 2016

Conjecture: sequence is equal to A038444 plus terms of the form 684917*10^k for k >= 0. - Chai Wah Wu, Sep 02 2017

Conjecture is true up to 4.8*10^18. - Giovanni Resta, Sep 03 2017

Examples

			684917 is in the sequence because 684917^3 = 321302302131323213.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..130

Crossrefs

Cf. A000578 (the cubes: n^3), A038444, A277960 (analog for squares), A278936 (cubes of the terms: a(n)^3).

Cf. A031997 (the odd terms).

Programs

Magma

[n: n in [1..2*10^7] | Max(Intseq(n^3)) eq 3]; // Vincenzo Librandi, Dec 03 2016

Mathematica

Select[Range[11 10^6],Max[IntegerDigits[#^3]]==3&] (* Harvey P. Dale, Feb 11 2025 *)

PARI

select(n->vecmax(digits(n^3))==3, vector(1000000, n, n))

Formula

a(n)^3 = A278936(n).