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A125520
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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.
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1
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3, 75, 825, 8835, 89235, 898335, 8992335, 89983335, 899923335, 8999833335, 89999233335, 899998333335, 8999992333335, 89999983333335, 899999923333335, 8999999833333335, 89999999233333335, 899999998333333335, 8999999992333333335, 89999999983333333335, 899999999923333333335
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OFFSET
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1,1
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LINKS
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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).
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FORMULA
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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.
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A125521 (minimal difference).
Sequence in context: A265956 A189805 A230145 * A163131 A060869 A012491
Adjacent sequences: A125517 A125518 A125519 * A125521 A125522 A125523
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KEYWORD
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nonn,easy,base
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AUTHOR
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Tanya Khovanova and Sergei Bernstein, Dec 29 2006
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STATUS
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approved
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