A307588 Numbers k such that the digits of k^(1/3) begin with k.

0, 1, 31, 999, 1000, 31622, 999999, 1000000, 31622776, 999999999, 1000000000, 31622776601, 999999999999, 1000000000000, 31622776601683, 999999999999999, 1000000000000000, 31622776601683792, 31622776601683793, 999999999999999999, 1000000000000000000

Offset: 1

Author

Dmitry Kamenetsky, Apr 17 2019

Keywords

• nonn
• base

Comments

Program is in A307371.

The subsequence {31, 31622, 31622776, 31622776601, 31622776601683, ...} looks like this subsequence of A052210 {32, 31623, 316228, 3162278, 31622777, ..., 316227766016838, ...}. - Bernard Schott, May 04 2019

Examples

			31622^(1/3) = 31.62251..., which begins with "31622", so 31622 is in the sequence.
The seeming pattern a(3k) = floor(10^(3k-3/2)), a(3k+1) = 10^(3k) - 1, a(3k+2) = 10^(3k), is broken at a(18) = a(19) - 1 = floor(10^(33/2)) - 1. - _Jon E. Schoenfield_, May 01 2019
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1172

Crossrefs

Cf. A307371, A307600.

Cf. A052210 (analog for 3rd power instead of 1/3).

Extensions

a(10)-a(21) from Jon E. Schoenfield, May 01 2019