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A239320
Ternary happy numbers.
3
1, 3, 9, 13, 17, 23, 25, 27, 31, 35, 37, 39, 47, 51, 53, 59, 61, 65, 69, 71, 73, 75, 77, 79, 81, 85, 89, 91, 93, 101, 105, 107, 109, 111, 117, 137, 141, 143, 153, 155, 159, 161, 167, 169, 173, 177, 179, 181, 183, 185, 187, 191, 195, 197, 207, 209, 213
OFFSET
1,2
COMMENTS
Numbers where the trajectory of iterated application of A006287 ends at the fixed point 1.
LINKS
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
Sequence in context: A077791 A176393 A345460 * A243656 A363406 A240108
KEYWORD
nonn,base,easy
AUTHOR
Jiri Klepl, Apr 13 2014
STATUS
approved