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

1,3

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

Crossrefs

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

Sequence in context: A102695 A252481 A308854 * A048024 A048002 A256523

Adjacent sequences: A144579 A144580 A144581 * A144583 A144584 A144585

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 17 2008

Status

approved