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3-Factorions: equal to the sum of the triple factorials of their digits in base 10.
4

%I #9 May 31 2023 12:46:09

%S 1,2,3,4,81,82,83,84

%N 3-Factorions: equal to the sum of the triple factorials of their digits in base 10.

%C Sequence is complete. - _Giovanni Resta_, Mar 21 2013

%e 81 -> 8!!! + 1!!! = 8*5*2 + 1 = 80 + 1 = 81.

%p P:=proc(n,m) local a,b,i,j,k,x,w; for i from 1 by 1 to n do a:=0; b:=0; w:=0; k:=i; while k>0 do w:=k-(trunc(k/10)*10); j:=w; x:=w-m; if w=0 then b:=1; else while x>0 do j:=j*x; x:=x-m; od; b:=j; fi; a:=a+b; k:=trunc(k/10); od; if a=i then lprint(i,a); fi; od; end: P(1000,3);

%t stfQ[n_]:=n==Total[Times@@Range[#,1,-3]&/@IntegerDigits[n]]; Select[Range[100],stfQ] (* _Harvey P. Dale_, May 31 2023 *)

%Y Cf. A007661, A014080, A097653, A173574-A173577

%K easy,fini,full,nonn,base

%O 1,2

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Feb 22 2010