A336890 Numbers that eventually reach the fixed point 8208 under "x --> sum of the fourth powers of digits of x".

12, 17, 21, 46, 64, 71, 102, 107, 120, 137, 145, 154, 170, 173, 201, 210, 224, 242, 279, 288, 297, 317, 349, 357, 371, 375, 379, 394, 397, 406, 415, 422, 439, 451, 460, 493, 514, 537, 541, 573, 599, 604, 640, 701, 710, 713, 729, 731, 735, 739, 753, 792, 793, 828, 882, 927, 934, 937, 943, 959, 972, 973, 995

Offset: 1

Author

Sergio Falcon, Aug 07 2020

Keywords

• nonn
• base

Examples

			12 --> 1^4+2^4 = 17 --> 1^4+7^4 = 2402 --> 2^4+4^4+0^4+2^4 = 288 --> 2^4+8^4+8^4 = 8208.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A219111, A031185, A031184.

Programs

Maple

V:= Vector(32805): V[8208]:= true:
g:= proc(n) local L, t;
  add(t^4, t = convert(n,base,10))
end proc:
f:= proc(n) local x,S; global V;
  if n <= 32805 then
     if V[n] <> 0 then return V[n]
     else S:= [n]
     fi
  else S:= []
  fi;
  x:= n;
  do
    x:= g(x);
    if V[x] <> 0 then
       V[S]:= V[x];
       return V[x]
    elif member(x,S) then
       V[S]:= false;
       return false
    fi;
    if x <= 32805 then S:= [op(S), x] fi;
  od;
end proc;
select(f, [$1..10000]); # Robert Israel, Sep 03 2020

Mathematica

okQ[n] := MemberQ[NestList[Total[IntegerDigits[#]^4]&, n, 30], 8208]; Select[Range[1000], okQ]