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

Author

Jiri Klepl, Apr 13 2014

Keywords

• nonn
• base
• easy

Comments

Numbers where the trajectory of iterated application of A006287 ends at the fixed point 1.

Examples

			13 is a ternary happy number because 13=111_3 -> 1 + 1 + 1 = 3 = 10_3 -> 1 + 0 = 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.

Crossrefs

Cf. A007770, A240849.

Programs

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 *)