A294664 Numbers n such that the largest digit of n^3 is 4.

7, 68, 70, 324, 680, 700, 3240, 6800, 7000, 7618, 31177, 32400, 52308, 68000, 69314, 70000, 76180, 311770, 324000, 353068, 523080, 680000, 693140, 700000, 756658, 761800, 1039247, 2715974, 2732441, 3117700, 3240000, 3511617, 3530680, 4689368, 5230800, 6800000, 6931400, 7000000

Offset: 1

Author

M. F. Hasler, Nov 12 2017

Keywords

• nonn
• base

Comments

For any term a(n), all numbers of the form a(n)*10^k, k >= 0, are in this sequence. Primitive terms, i.e., not of this form (or equivalently: without trailing '0'), are 7, 68, 324, 7618, 31177, 52308, 69314, 353068, 756658, 1039247, 2715974, 2732441, 3511617, 4689368, 7571814, 12811968, 15904541, ...

All terms have last nonzero digit 1, 4, 7 or 8 and leading digit <= 7. - Robert Israel, Nov 13 2017

The number formed by the first m digits of a term is always less than c*10^m with c = (4/9)^(1/3) = .7631428283688879... - M. F. Hasler, Nov 13 2017

Examples

			7 is in the sequence because the largest digit of 7^3 = 343 is 4.
		

Crossrefs

Cf. A294663 (the corresponding cubes), A278937, A294665, A294996 - A294999 (analog for digits 3, 5, 6 - 9); A277961 (analog for squares).

Cf. A000578 (the cubes).

Programs

Maple

select(n -> max(convert(n^3,base,10))=4, [$1..10^6]); # Robert Israel, Nov 13 2017

PARI

for(n=1,2e8, vecmax(digits(n^3))==4&&print1(n","))