A239320 Ternary happy numbers.

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

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

Cf. A007770, A240849.

Sequence in context: A077791 A176393 A345460 * A243656 A363406 A240108

Adjacent sequences: A239317 A239318 A239319 * A239321 A239322 A239323

Keyword

nonn,base,easy

Author

Jiri Klepl, Apr 13 2014

Status

approved