A144582 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

(Haskell)

a144582 n = a144582_list !! (n-1)