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
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
Programs
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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]