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A224220
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a(n) = smallest number k with property that if the base-n expansion of k is reversed, the result is a nontrivial multiple of k.
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1
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32, 75, 8, 245, 12, 21, 16, 1089, 15, 1859, 21, 39, 28, 4335, 24, 6137, 24, 57, 40, 11109, 33, 115, 39, 45, 52, 22707, 35, 27869, 40, 93, 64, 55, 51, 47915, 57, 111, 76, 65559, 48, 75809, 56, 129, 88, 99405, 69, 329, 60, 119, 65, 143259, 72, 265, 63, 95, 112, 198417, 87, 219539
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OFFSET
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3,1
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COMMENTS
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In other words, k divides (reversal of k in base n), and (k-reversed)/k > 1.
The numbers are written in base 10.
Theorem: The length of k (in base n) is 2 iff n>=5 and n+1 is composite, otherwise 4.
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REFERENCES
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N. J. A. Sloane, paper in preparation.
See A214927 for further references and links.
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LINKS
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FORMULA
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If n=3 or n>3 and n+1 is prime, a(n) = (n^2-1)(n+1) (cf. A152619).
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EXAMPLE
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The numbers a(n) for n = 3, ..., 11 written in base n are 1012, 1023, 13, 1045, 15, 25, 17, 1089, 14.
For example, 1012 (base 3) = 32 (base 10), and 2101 (base 3) = 64 (base 10) = 2*32.
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MATHEMATICA
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Table[k = 2; While[Nand[IntegerQ@ #, # != 1] &[FromDigits[#, n]/k] &@ Reverse@ IntegerDigits[k, n], k++]; k, {n, 3, 60}] (* Michael De Vlieger, Feb 26 2017 *)
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PROG
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(PARI) isok(k, n) = {my(rk = fromdigits(Vecrev(digits(k, n)), n)); !(rk % k) && (rk > k); }
a(n) = {my(k = 1); while (!isok(k, n), k++); k; } \\ Michel Marcus, Feb 26 2017
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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