

A125521


a(n) is the minimal difference between two distinct ndigit 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
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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(n1)/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[#res1])); 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



