A174570 Numbers n such that sum of squares of factorials of digits of n is a power of 2.

1, 2, 10, 11, 22, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 2222, 10002, 10012, 10020, 10021, 10102, 10112, 10120, 10121, 10200, 10201, 10210, 10211, 11002, 11012, 11020, 11021, 11102, 11112, 11120, 11121, 11200, 11201, 11210, 11211, 12000, 12001, 12010, 12011, 12100, 12101, 12110, 12111, 20000, 20001, 20010

Offset

1,2

Links

Table of n, a(n) for n=1..49.

Example

10012 is in the sequence because (1!)^2 +(0!)^2 +(0!)^2 +(1!)^2 +(2!)^2 = 8 = 2^3.

Maple

with(numtheory):for n from 1 to 100000 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:= evalf(log[2](s));
  if floor(q)= q then printf(`%d, `, n):else fi:od:

Prog

(Sage) A174570 = list(n for n in IntegerRange(1, 10**5) if sum(factorial(d)**2 for d in n.digits()).is_power_of(2))

Crossrefs

Sequence in context: A356520 A174569 A179884 * A072545 A023151 A342535

Adjacent sequences: A174567 A174568 A174569 * A174571 A174572 A174573

Keyword

nonn,base

Author

Michel Lagneau, Nov 29 2010

Status

approved