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A031877
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Nontrivial reversal numbers (numbers which are integer multiples of their reversals), excluding palindromic numbers and multiples of 10.
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13
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8712, 9801, 87912, 98901, 879912, 989901, 8799912, 9899901, 87128712, 87999912, 98019801, 98999901, 871208712, 879999912, 980109801, 989999901, 8712008712, 8791287912, 8799999912, 9801009801, 9890198901, 9899999901
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OFFSET
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1,1
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REFERENCES
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W. W. R. Ball and H. S. M. Coxeter. Mathematical Recreations and Essays (1939, page 13); 13th ed. New York: Dover, pp. 14-15, 1987.
G. H. Hardy, A Mathematician's Apology (Cambridge Univ. Press, 1940, reprinted 2000), pp. 104-105 (describes this problem as having "nothing in [it] which appeals much to a mathematician.").
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LINKS
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Table of n, a(n) for n=1..22.
Patrick De Geest, Palindromic Products of Integers and their Reversals
Lara Pudwell, Digit Reversal Without Apology, Mathematics Magazine, Vol. 80 (2007), pp. 129-132.
Eric Weisstein's World of Mathematics, Reversal.
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MATHEMATICA
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fQ[n_] := Block[{id = IntegerDigits@n}, Mod[n, FromDigits@ Reverse@id] == 0 && n != FromDigits@ Reverse@ id && Mod[n, 10] > 0]; k = 1; lst = {}; While[k < 10^9, If[fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst [From Robert G. Wilson v, Jun 11 2010]
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CROSSREFS
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See A008919 for reversals.
Cf. A031877, A169824, A214927.
Union of A222814 and A222815.
Sequence in context: A203737 A214487 A170796 * A222815 A035909 A031852
Adjacent sequences: A031874 A031875 A031876 * A031878 A031879 A031880
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KEYWORD
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nonn,base
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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More terms from Jud McCranie, Aug 15 2001
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STATUS
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approved
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