A318235 Ascending list of base-60 happy numbers written in base 10.

1, 54, 60, 237, 1134, 2208, 2916, 3240, 3258, 3423, 3600, 3727, 4022, 4316, 5990, 6639, 6971, 7267, 7505, 7621, 7693, 7856, 7988, 8011, 8249, 8957, 9073, 10570, 10857, 10986, 11163, 11193, 11730, 12615, 12786, 13859, 14220, 14390, 14399, 14714, 15011, 15070

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

E. S. Williams, Further Generalizations of Happy Numbers, Mathematical Association of America, (2016).

Example

1134 is a term because the base-60 iteration of A007770 gives 1134 -> 3240 -> 2916 -> 3600 -> 1.

Maple

b:= proc() false end:
q:= proc(n) local m, s; m, s:= n, {};
      do if m=1 then return true
       elif m in s or b(m) then b(n):= true; return false
       else s, m:= {s[], m}, add(i^2, i=convert(m, base, 60))
         fi
      od
    end:
select(q, [$1..20000])[];  # Alois P. Heinz, Jan 05 2022

Mathematica

Select[Range[15100], FixedPoint[Total[IntegerDigits[#, 60]^2] &, #, 60] == 1 &] (* Michael De Vlieger, Jan 04 2022 *)

Prog

(PARI) sumsod60(n) = my(d=digits(n, 60)); sum(i=1, #d, d[i]^2)
is(n) = my(v=[n]); while(1, v=concat(v, sumsod60(v[#v])); if(vecsort(v)!=vecsort(v, , 8) && n!=1, return(0)); if(vecmin(v)==1, return(1))) \\ Felix Fröhlich, Aug 22 2018

Crossrefs

Base-60 iteration of A007770.

Sequence in context: A095521 A095511 A095501 * A158989 A088489 A025331

Adjacent sequences: A318232 A318233 A318234 * A318236 A318237 A318238

Keyword

nonn,base

Author

Cole Ditzler, Aug 21 2018

Status

approved