A125520 a(n) is the maximal difference between two distinct n-digit numbers with the property that when one of them is typed into a calculator and rotated 180 degrees, the other one is seen.

3, 75, 825, 8835, 89235, 898335, 8992335, 89983335, 899923335, 8999833335, 89999233335, 899998333335, 8999992333335, 89999983333335, 899999923333335, 8999999833333335, 89999999233333335, 899999998333333335, 8999999992333333335, 89999999983333333335, 899999999923333333335

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Index entries for sequences related to calculator display

Index entries for linear recurrences with constant coefficients, signature (11,0,-110,100).

Formula

If n is greater than 2 and even, than a(n) is 8 followed by (n / 2) - 2 nines followed by another 8 followed by (n / 2) - 1 threes followed by 5. If n is greater than 2 and odd, than a(n) is 8 followed by (n / 2) - 1.5 nines followed by a 2 followed by (n / 2) - 1.5 threes followed by a 5.

Example

a(2) = 75. If someone types 91 into a calculator and rotates it 180 degrees, they will get 16. 91 - 16 = 75. It is easy to check that no larger differences can be obtained.

Mathematica

LinearRecurrence[{11, 0, -110, 100}, {3, 75, 825, 8835}, 30] (* Harvey P. Dale, Nov 13 2021 *)

Prog

(PARI) first(n) = {my(res = List([3, 75, 825, 8835, 89235, 898335, 8992335, 89983335])); for(i = #res + 1, n, listput(res, 11*res[#res] - 110*res[#res-2] + 100 * res[#res-3])); res} \\ David A. Corneth, Aug 05 2020

Crossrefs

Cf. A125521 (minimal difference).

Sequence in context: A189805 A230145 A343808 * A163131 A060869 A012491

Adjacent sequences: A125517 A125518 A125519 * A125521 A125522 A125523

Keyword

nonn,easy,base

Author

Tanya Khovanova and Sergei Bernstein, Dec 29 2006

Status

approved