A240849 Quinary happy numbers.

1, 5, 7, 11, 19, 23, 25, 27, 33, 35, 41, 43, 49, 51, 55, 79, 81, 83, 91, 93, 95, 99, 103, 109, 115, 119, 121, 123, 125, 127, 133, 135, 141, 143, 149, 153, 157, 159, 161, 165, 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

Offset: 1

Author

Jiri Klepl, Apr 13 2014

Keywords

• nonn
• base
• easy

Comments

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.

Examples

			19 is a quinary happy number because 19=34_5 -> 3^2 + 4^2 = 25 = 100_5 -> 1+0+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, A239320.

Programs

Maple

isA240849 := proc(n)
    t := SqrdB5(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 := A276191(t) ;
    end do:
end proc:
for n from 1 to 300 do
    if isA240849(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Aug 24 2016

Mathematica

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