A097569 Right-truncatable Harshad numbers (zeros not permitted).

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 18, 21, 24, 27, 36, 42, 45, 48, 54, 63, 72, 81, 84, 126, 216, 243, 247, 364, 423, 481, 486, 846, 2478, 8463, 24786

Offset: 1

Author

Jason Earls, Aug 28 2004

Keywords

• base
• nonn
• fini
• full

Comments

Harshad numbers in which repeatedly deleting the rightmost digit gives a Harshad number at every step until a single-digit Harshad number remains. Sequence is finite with 24786 being the last term.

24786 can be proved to be the last term by a genetic approach (constructing the whole tree). - Carlos Rivera, Sep 19 2004

Crossrefs

Cf. A005349.

Programs

Mathematica

harQ[n_]:=Module[{idn=IntegerDigits[n]},!MemberQ[idn,0]&&Divisible[n, Total[ idn]]]; rtQ[n_]:=Module[{idn=IntegerDigits[n],c}, c=Table[ FromDigits[ Take[ idn,i]],{i,Length[idn]}];And@@(harQ/@c)]; Select[ Range[25000],rtQ] (* Harvey P. Dale, Oct 07 2013 *)