A058226 - OEIS

%I #25 Aug 20 2024 23:09:49

%S 1,2,3,4,5,6,7,8,9,10,11,12,14,15,18,20,21,23,24,31,34,36,37,39,40,43,

%T 45,53,54,57,59,61,69,72,73,77,78,81,85,89,91,121,127,144,166,169,211,

%U 219,231,239,257,267,271,331,337,353,361,413,481,523,571,661,721,1093,1291,3097

%N Panconsummate numbers (consummate in all bases >=2).

%C No more terms <= 358000 and probably the list shown is complete.

%C Next term >= 10^6. - _Giovanni Resta_, Jan 05 2014

%C Next term >= 10^7. - _Jake L Lande_, Aug 06 2024

%t consQ[n_, b_] := Catch@Block[{nd = 1, from, to},While[Ceiling[b^(nd - 1)/n]>Min[nd(b - 1), Floor[(b^nd - 1)/n]], nd++];While[(from = Ceiling[b^(nd - 1)/n]) <= (to = Min[nd (b - 1), Floor[(b^nd - 1)/n]]),Do[If[k == Plus @@ IntegerDigits[k  n, b], Throw@True], {k, from, to}]; nd++]; False];

%t panConQ[n_] := Catch@Block[{}, Do[If[! consQ[n, b], Throw@False], {b, 2, n - 1}]; True]; Select[Range[3097], panConQ]  (* code supplied by _Giovanni Resta_, Aug 06 2024 *)

%Y Complement of A058225.

%K nonn,base,nice

%O 1,2

%A _David W. Wilson_, Jan 17 2001