A136853 Numbers k such that k and k^2 use only the digits 0, 1, 3 and 9.

0, 1, 3, 10, 30, 100, 300, 1000, 3000, 10000, 30000, 100000, 300000, 1000000, 3000000, 10000000, 30000000, 100000000, 300000000, 1000000000, 3000000000, 10000000000, 30000000000, 100000000000, 300000000000, 1000000000000, 3000000000000, 10000000000000, 30000000000000, 100000000000000, 300000000000000

Offset

1,3

Comments

Generated with DrScheme.

Links

Table of n, a(n) for n=1..31.

Jovan Radenkovicc, Formula for the OEIS sequence A136853 (on Reddit)

Jonathan Wellons, Tables of Shared Digits [archived]

Index entries for linear recurrences with constant coefficients, signature (0,10).

Formula

From Jovan Radenkovicc, Nov 16 2024: (Start)

For n>=1, a(2*n) = 10^(n-1) and a(2*n+1) = 3*10^(n-1).

a(n) = 10*a(n-2) for n>=4.

For proof see the Reddit link. (End)

Example

300000000000000^2 = 90000000000000000000000000000.

Crossrefs

Sequence in context: A136841 A136846 A004663 * A361911 A215287 A316764

Adjacent sequences: A136850 A136851 A136852 * A136854 A136855 A136856

Keyword

base,easy,nonn

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Status

approved