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A218030 Numbers k equal to half of the product of the nonzero (base-10) digits of k^2. 2
2, 5, 54, 648, 2160, 337169025526136832000, 685506275314921762068267522458966662115416623590907309075726336000000, 46641846972427276691124922228108091690332947069125333309512419901440000000000 (list; graph; refs; listen; history; text; internal format)
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
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 digit-product to the original number is 2. Related to A218072.
Sequence in context: A206848 A081482 A134475 * A114029 A013171 A073422
KEYWORD
nonn,base
AUTHOR
Nels Olson, Oct 18 2012
STATUS
approved

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Last modified February 25 12:52 EST 2024. Contains 370327 sequences. (Running on oeis4.)