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A240849 Quinary happy numbers.

%I A240849 #22 May 28 2020 05:27:25
%S A240849 1,5,7,11,19,23,25,27,33,35,41,43,49,51,55,79,81,83,91,93,95,99,103,
%T A240849 109,115,119,121,123,125,127,133,135,141,143,149,153,157,159,161,165,
%U A240849 169,171,173,175,181,189,193,197,201,203,205,209,213,215,217,219,221,223,229,231,233,237,241,243,245,249
%N A240849 Quinary happy numbers.
%C A240849 Numbers for which the repeated application of the operation "Sum the squares of the digits of the base-5 representation" is trapped by (ends at) the fixed point 1.
%H A240849 Amiram Eldar, <a href="/A240849/b240849.txt">Table of n, a(n) for n = 1..10000</a>
%H A240849 H. G. Grundmann, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Grundman/grundman7.html">Semihappy Numbers</a>, J. Int. Seq. 13 (2010), 10.4.8.
%e A240849 19 is a quinary happy number because 19=34_5 -> 3^2 + 4^2 = 25 = 100_5 -> 1+0+0 = 1.
%p A240849 isA240849 := proc(n)
%p A240849     t := SqrdB5(n) ;
%p A240849     tloo := {} ;
%p A240849     for i from 1 do
%p A240849         if t = 1 then
%p A240849             return true;
%p A240849         end if;
%p A240849         if t in tloo then
%p A240849             return false;
%p A240849         end if;
%p A240849         tloo := tloo union {t} ;
%p A240849         t := A276191(t) ;
%p A240849     end do:
%p A240849 end proc:
%p A240849 for n from 1 to 300 do
%p A240849     if isA240849(n) then
%p A240849         printf("%d,",n) ;
%p A240849     end if;
%p A240849 end do: # _R. J. Mathar_, Aug 24 2016
%t A240849 happyQ[n_, b_] := NestWhile[Plus @@ (IntegerDigits[#, b]^2) &, n, UnsameQ, All] == 1; Select[Range[250], happyQ[#, 5] &] (* _Amiram Eldar_, May 28 2020 *)
%Y A240849 Cf. A007770, A239320.
%K A240849 nonn,base,easy
%O A240849 1,2
%A A240849 _Jiri Klepl_, Apr 13 2014