%I #6 Mar 30 2012 17:27:25
%S 3,49,73,88,97,198,840,1479,2425,5277,18799
%N Balanced ternary Keith numbers.
%C Only terms in common with base 3 Keith numbers (A188195) for the range examined are 3 and 840.
%C If the sum of balanced ternary digits of a positive number is 0 or less, then the recurrence from the digits soon becomes consistently negative and the number in question is not a Keith number in balanced ternary.
%e The number 49 in balanced ternary is {1, -1, -1, 1, 1}. The pentanacci-like sequence continues 1, 1, 3, 7, 13, 25, 49, thus 49 is a Keith number in balanced ternary.
%t (* First run program at A065363 to define balTernDigits *) keithFromListQ[n_Integer, digits_List] := Module[{seq = digits, curr = digits[[-1]], ord = Length[digits]}, While[curr < n, curr = Plus@@Take[seq, -ord]; AppendTo[seq, curr]]; Return[seq[[-1]] == n]]; Select[Range[3, 19683], Plus@@balTernDigits[#] > 0 && keithFromListQ[#, balTernDigits[#]] &]
%K nonn,base
%O 1,1
%A _Alonso del Arte_, Mar 29 2011