A125521 - OEIS

A125521

a(n) is the minimal difference between two distinct n-digit numbers with property that when one of them is typed into a calculator and rotated 180 degrees, the other one is seen.

3, 6, 30, 60, 300, 600, 3000, 6000, 30000, 60000, 300000, 600000, 3000000, 6000000, 30000000, 60000000, 300000000, 600000000, 3000000000, 6000000000, 30000000000, 60000000000, 300000000000, 600000000000, 3000000000000, 6000000000000, 30000000000000, 60000000000000, 300000000000000

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

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..29.

Index entries for sequences related to calculator display

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

FORMULA

If n is even, a(n) is 6 followed by (n - 2) / 2 zeros. If n is odd, a(n) is 3 followed by (n - 1) / 2 zeros.

So a(n) = 3 * 10^(floor(n-1)/2) * 2^(1 - n (mod 2)).

From David A. Corneth, Aug 05 2020: (Start)

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

G.f.: (3*x + 6*x^2)/(1 - 10*x^2). (End)

EXAMPLE

a(3) = 30. If one types 595 into a calculator and rotates it 180 degrees, they will get 565. 595 - 565 = 30. With a little thought, it is provable that 30 is the smallest possible difference.

MATHEMATICA

LinearRecurrence[{0, 10}, {3, 6}, 30] (* Amiram Eldar, Aug 05 2020 *)

PROG

(PARI) first(n) = my(res = List([3, 6])); for(i = #res + 1, n, listput(res, 10*res[#res-1])); res \\ David A. Corneth, Aug 05 2020

CROSSREFS

Cf. A125520 (maximal difference).

Sequence in context: A136939 A136944 A136946 * A211168 A355989 A215294

Adjacent sequences: A125518 A125519 A125520 * A125522 A125523 A125524

KEYWORD

nonn,easy,base

AUTHOR

Tanya Khovanova and Sergei Bernstein, Dec 29 2006

STATUS

approved