A058226 Panconsummate numbers (consummate in all bases >=2).

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, 45, 53, 54, 57, 59, 61, 69, 72, 73, 77, 78, 81, 85, 89, 91, 121, 127, 144, 166, 169, 211, 219, 231, 239, 257, 267, 271, 331, 337, 353, 361, 413, 481, 523, 571, 661, 721, 1093, 1291, 3097

Offset

1,2

Comments

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

Next term >= 10^6. - Giovanni Resta, Jan 05 2014

Next term >= 10^7. - Jake L Lande, Aug 06 2024

Links

Table of n, a(n) for n=1..66.

Mathematica

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];
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 *)

Crossrefs

Complement of A058225.

Sequence in context: A028828 A334139 A178864 * A172974 A066255 A330236

Adjacent sequences: A058223 A058224 A058225 * A058227 A058228 A058229

Keyword

nonn,base,nice

Author

David W. Wilson, Jan 17 2001

Status

approved