

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

Michael S. Branicky, Table of n, a(n) for n = 1..12 (all terms < 10^300)
Michael S. Branicky, Python program
Giovanni Resta, C program for this and related sequences


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];
p2 *= 2]; Sort[L] (* Giovanni Resta, Oct 19 2012 *)


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.
Sequence in context: A206848 A081482 A134475 * A114029 A013171 A073422
Adjacent sequences: A218027 A218028 A218029 * A218031 A218032 A218033


KEYWORD

nonn,base


AUTHOR

Nels Olson, Oct 18 2012


STATUS

approved



