

A218030


Numbers k equal to half of the product of the nonzero (base10) digits of k^2.


2



2, 5, 54, 648, 2160, 337169025526136832000, 685506275314921762068267522458966662115416623590907309075726336000000, 46641846972427276691124922228108091690332947069125333309512419901440000000000
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OFFSET

1,1


COMMENTS

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.


LINKS



EXAMPLE

For n=5, n^2 is 25; the product of the digits of 25 is 2*5 = 10, which is equal to 2*n.


MATHEMATICA

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];


PROG

(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


CROSSREFS

Special case of A218013 where the ratio of the digitproduct to the original number is 2. Related to A218072.


KEYWORD

nonn,base


AUTHOR



STATUS

approved



