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A218030
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Numbers k equal to half of the product of the nonzero (base-10) digits of k^2.
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2
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2, 5, 54, 648, 2160, 337169025526136832000, 685506275314921762068267522458966662115416623590907309075726336000000, 46641846972427276691124922228108091690332947069125333309512419901440000000000
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OFFSET
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1,1
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COMMENTS
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The first 5 terms of the sequence were found by the author around 1980 using his Commodore PET computer. He found the subsequent terms in 1991 by means of an improved program. The author has always referred to these as the "Faithy numbers" after his mother Faith who posed the problem.
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LINKS
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EXAMPLE
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For n=5, n^2 is 25; the product of the digits of 25 is 2*5 = 10, which is equal to 2*n.
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MATHEMATICA
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mx = 2^255; L = {};
p2 = 1; While[p2 < mx, Print["--> 2^", Log[2, p2]];
p3 = p2; While [p3 < mx,
p5 = p3; While[p5 < mx,
n = p5; While[n < mx,
If[2 n == Times @@ Select[IntegerDigits[n^2], # > 0 &],
AppendTo[L, n]; Print[n]]; n *= 7]; p5 *= 5]; p3 *= 3];
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PROG
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(PARI) is_A218030(n)={my(d=digits(n^2)); n*=2; for(i=1, #d, d[i]||next; n%d[i]&return; n\=d[i]); n==1} \\ M. F. Hasler, Oct 19 2012
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CROSSREFS
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Special case of A218013 where the ratio of the digit-product to the original number is 2. Related to A218072.
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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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