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

1,2

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.

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

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

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 *)

Crossrefs

Cf. A007770, A239320.

Sequence in context: A089785 A226383 A118386 * A116641 A288446 A213981

Adjacent sequences: A240846 A240847 A240848 * A240850 A240851 A240852

Keyword

nonn,base,easy

Author

Jiri Klepl, Apr 13 2014

Status

approved