

A173689


Numbers m such that the sum of square of factorial of decimal digits is square.


2



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 122, 202, 212, 220, 221, 244, 424, 442, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 2222, 3333, 3444, 4344, 4434, 4443, 4444, 5555, 6666, 6677, 6767, 6776, 6888, 7667, 7676, 7766, 7777, 8688, 8868, 8886, 8888, 9999
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Let the decimal expansion of m = d(0)d(1)...d(p). Numbers such that Sum_{k=0..p} (d(k)!)^2 is square.


LINKS

Jinyuan Wang, Table of n, a(n) for n = 1..1487


EXAMPLE

a(16) = 244 is in the sequence because (2!)^2 + (4!)^2 + (4!)^2 = 1156 = 34^2.


MAPLE

with(numtheory):for n from 0 to 10000 do:l:=length(n):n0:=n:s:=0:for m from
1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+(u!)^2:od: q:=sqrt(s):if
floor(q)= q then printf(`%d, `, n):else fi:od:


MATHEMATICA

Select[Range[0, 10000], IntegerQ[Sqrt[Total[(IntegerDigits[#]!)^2]]]&] (* Harvey P. Dale, Dec 19 2011 *)


CROSSREFS

Cf. A173687, A173688.
Sequence in context: A134853 A193407 A134810 * A004871 A059405 A191872
Adjacent sequences: A173686 A173687 A173688 * A173690 A173691 A173692


KEYWORD

nonn,base


AUTHOR

Michel Lagneau, Nov 25 2010


EXTENSIONS

Offset changed to 1 by Jinyuan Wang, Feb 26 2020


STATUS

approved



