OFFSET
1,2
COMMENTS
Numbers where the trajectory of iterated application of A006287 ends at the fixed point 1.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
H. G. Grundmann, Semihappy Numbers, J. Int. Seq. 13 (2010), 10.4.8.
EXAMPLE
13 is a ternary happy number because 13=111_3 -> 1 + 1 + 1 = 3 = 10_3 -> 1 + 0 = 1.
MAPLE
isA239320 := proc(n)
t := A006287(n) ;
tloo := {} ;
for i from 1 do
if t = 1 then
return true;
end if;
if t in tloo then
return false;
end if;
tloo := tloo union {t} ;
t := A006287(t) ;
end do:
end proc:
for n from 1 to 300 do
if isA239320(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Jun 13 2014
MATHEMATICA
happyQ[n_, b_] := NestWhile[Plus @@ (IntegerDigits[#, b]^2) &, n, UnsameQ, All] == 1; Select[Range[213], happyQ[#, 3] &] (* Amiram Eldar, May 28 2020 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Jiri Klepl, Apr 13 2014
STATUS
approved