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A161791
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Numbers k such that if k = a*b, then a+b = reversal(k) for some integers a,b > 1.
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1
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4, 72, 81, 94, 130, 994, 1210, 1930, 3420, 3640, 3910, 7420, 9360, 9994, 12600, 15300, 19930, 38520, 68800, 98010, 99220, 99994, 196200, 199930, 316710, 389520, 510300, 576900, 644400, 698620, 788310, 871200, 923400, 937210, 999994, 1020100, 1999930, 3246120, 3490200, 3899520
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OFFSET
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1,1
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COMMENTS
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Here, reversal(k), is k written backwards in decimal with leading zeros omitted. - Sean A. Irvine, Sep 15 2019
The sequence is infinite because 94, 994, 9994, ... , 99..94, ... are terms, (999..94 = 2 * 49..97 and 2 + 499..97 = 499..99). Also the numbers of form 130, 1930, 19930, ...., 199...930, ... are terms (130 = 5 * 26, 1930 = 5 * 386, 19930 = 5 * 3986, 199930 = 5 * 39986, ...). - Marius A. Burtea, Sep 16 2019
A third family: 38520, 389520, 3899520, ... , 389...9520, ... are terms because 38520 = 15 * 2568 and 15 + 2568 = 2583, also 389..9520 = 15 * 259..968 and 15 + 259..968 = 259..983. - Bernard Schott, Sep 16 2019
Another family: 3246120, 32406120, 324006120, 3240006120, 32400006120, ... In fact, 3240..06120 = 15 * 2160..0408 and 15 + 2160..0408 = 2160..0423, reversal of 3240..06120. - Bruno Berselli, Sep 17 2019
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LINKS
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EXAMPLE
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94 is in the list because 94 = 2 * 47 and 2 + 47 = 49 (reversal of 94).
Similarly, 3420 = 15 * 228 and 15 + 228 = 243 (reversal of 3420).
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PROG
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(PARI) isok(m) = {my(rm = fromdigits(Vecrev(digits(m)))); fordiv(m, d, if (d + m/d == rm, return (1)); ); return (0); } \\ Michel Marcus, Sep 16 2019
(Magma) [k: k in [1..4000000]| IsSquare(Seqint(Reverse(Intseq(k)))^2-4*k)]; // Marius A. Burtea, Sep 16 2019
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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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EXTENSIONS
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STATUS
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approved
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