A240849 - OEIS

%I #22 May 28 2020 05:27:25

%S 1,5,7,11,19,23,25,27,33,35,41,43,49,51,55,79,81,83,91,93,95,99,103,

%T 109,115,119,121,123,125,127,133,135,141,143,149,153,157,159,161,165,

%U 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 Quinary happy numbers.

%C 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 Amiram Eldar, <a href="/A240849/b240849.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 19 is a quinary happy number because 19=34_5 -> 3^2 + 4^2 = 25 = 100_5 -> 1+0+0 = 1.

%p isA240849 := proc(n)

%p     t := SqrdB5(n) ;

%p     tloo := {} ;

%p     for i from 1 do

%p         if t = 1 then

%p             return true;

%p         end if;

%p         if t in tloo then

%p             return false;

%p         end if;

%p         tloo := tloo union {t} ;

%p         t := A276191(t) ;

%p     end do:

%p end proc:

%p for n from 1 to 300 do

%p     if isA240849(n) then

%p         printf("%d,",n) ;

%p     end if;

%p end do: # _R. J. Mathar_, Aug 24 2016

%t happyQ[n_, b_] := NestWhile[Plus @@ (IntegerDigits[#, b]^2) &, n, UnsameQ, All] == 1; Select[Range[250], happyQ[#, 5] &] (* _Amiram Eldar_, May 28 2020 *)

%Y Cf. A007770, A239320.

%K nonn,base,easy

%O 1,2

%A _Jiri Klepl_, Apr 13 2014