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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. 1
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 A215294 A090932

Adjacent sequences:  A125518 A125519 A125520 * A125522 A125523 A125524

KEYWORD

nonn,easy,base

AUTHOR

Tanya Khovanova and Sergei Bernstein, Dec 29 2006

STATUS

approved

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Last modified September 21 12:33 EDT 2020. Contains 337272 sequences. (Running on oeis4.)