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Balanced ternary Keith numbers.
1

%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