cp's OEIS Frontend

A003621 Number of iterations until n reaches 1 or 4 under x goes to sum of squares of digits map.

%I A003621 M4764 #30 Apr 11 2019 22:49:38
%S A003621 0,1,11,0,8,13,5,9,10,1,2,9,2,10,10,7,9,9,4,1,9,10,3,2,7,9,10,3,6,11,
%T A003621 2,3,10,8,9,12,6,7,11,8,10,2,8,4,11,8,9,10,4,8,10,7,9,11,9,8,10,5,8,
%U A003621 13,7,9,12,8,8,11,6,2,12,5,9,10,6,9,10,6,5,4,3,9
%N A003621 Number of iterations until n reaches 1 or 4 under x goes to sum of squares of digits map.
%D A003621 J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 13.
%D A003621 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003621 Seiichi Manyama, <a href="/A003621/b003621.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%H A003621 A. Porges, <a href="/A003621/a003621.pdf">A set of eight numbers</a>, Amer. Math. Monthly, 52 (1945), 379-382. [Annotated scanned copy]
%H A003621 Arthur Porges, <a href="http://www.jstor.org/stable/2304639">A set of eight numbers</a>, Amer. Math. Monthly 52 (1945), 379-382.
%F A003621 a(n) = 0 if n = 1 or 4, otherwise a(n) = 1 + a(A003132(n)). - _Robert Israel_, Apr 11 2019
%p A003621 f:= n -> convert(map(t -> t^2, convert(n,base,10)),`+`):
%p A003621 g:= proc(n) option remember;
%p A003621   if n = 1 or n = 4 then 0 else 1 + procname(f(n)) fi
%p A003621 end proc:
%p A003621 map(g, [$1..100]); # _Robert Israel_, Apr 11 2019
%t A003621 Table[Length[NestWhileList[Total[IntegerDigits[#]^2]&,n,#!=1&&#!=4&]],{n,80}]-1 (* _Harvey P. Dale_, Dec 31 2016 *)
%Y A003621 Cf. A000216, A000218, A300081, etc.
%Y A003621 Cf. A003132.
%K A003621 nonn,base
%O A003621 1,3
%A A003621 _N. J. A. Sloane_, _Mira Bernstein_