A144582 Numbers having the same leading decimal digit as their cube.

0, 1, 10, 11, 12, 28, 29, 32, 33, 34, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287

Offset: 1

Author

Reinhard Zumkeller, Aug 17 2008

Keywords

• nonn
• base

Comments

For k > 0, write k = s * 10^t, 1 <= s < 10, then k is a term if and only if s is in [1, 2^(1/3)) U (20^(1/3), 3) U (30^(1/3), 40^(1/3)) U (30^(2/3), 10). - Jianing Song, Dec 26 2022

Examples

			a(13)=99 and 970299=99^3 start both with 9.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000030, A002994, A000578, A089951, A256523 (subsequence).

Programs

Haskell

a144582 n = a144582_list !! (n-1)
a144582_list = [x | x <- [0..], a000030 x == a000030 (x ^ 3)]
-- Reinhard Zumkeller, Apr 01 2015

Mathematica

Select[Range[0,300],First[IntegerDigits[#]]== First[IntegerDigits[#^3]]&]  (* Harvey P. Dale, Mar 14 2011 *)

PARI

isok(n) = (n == 0) || (digits(n)[1] == digits(n^3)[1]); \\ Michel Marcus, Mar 18 2015

Formula

A000030(a(n)) = A002994(a(n)) = A000030(A000578(a(n))).