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 A274231 Ternary representation with index set {0, 1, 5}. 0
 0, 1, 3, 4, 5, 8, 9, 10, 12, 13, 14, 15, 16, 17, 20, 24, 25, 27, 28, 29, 30, 31, 32, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 60, 61, 65, 72, 73, 75, 76, 77, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 101, 105, 106, 108, 109, 110, 111, 112, 113 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A number m is in the sequence if m = b_r * 3^r + b_(r-1) * 3^(r-1) + ... + b_0, where b_i is in {0, 1, 5}. The maximal sets of consecutive numbers in this sequences can be associated with the Fibonacci numbers (A000045) and Pell numbers (A000129). REFERENCES Thomas Koshy, Pell and Pell-Lucas Numbers with Applications, Springer New York Heidelberge Dordrecht London, Cambridge, 2014, p.193 LINKS Wipawee Tangjai, Density and spacing properties of some families of non-standard ternary representations, Doctoral Dissertation, University of Illinois at Urbana-Champaign, 2014. FORMULA G.f.:  (1/(1-x))(1-x^2+x^3)(1-x^(2*3)+x^(3^2))...(1-x^(2*3^k)+x^(3^(k+1)) ... EXAMPLE a(1) = 0; a(2) = 3*a(1) + 1 = 1; a(3) = 3*a(2) = 3; a(4) = 3*a(2) + 1; a(5) = 3*a(1) + 5 = 5; a(6) = 3*a(2) + 5. MATHEMATICA Select[Union[Table[FromDigits[IntegerDigits[k, 3] /. 2 -> 5, 3], {k, 0, 3^5 - 1}]], # < 3^5 &] (* Giovanni Resta, Jun 24 2016 *) PROG (R) #This program generates numbers from a(1) to a(135) #it can be increased by changing number of k m3<-function(x, k){   for(j in 1:k){   A=array(3*x)   B=array(3*x+1)   C=array(3*x+5)   for(i in 2:length(x)){     A=c(A, 3*x[i])     B=c(B, 3*x[i]+1)     C=c(C, 3*x[i]+5)     result=sort(union(x, union(A, union(B, C))), decreasing = FALSE)    }   x=result   }   return(result)   } S=array(0) U=m3(S, 3) #row r-1 V=m3(S, 4) #row r up=ceiling((V[length(V)]-5)/3) # find the max element in r that less than in r-1 Y1=V[V

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Last modified June 20 09:27 EDT 2019. Contains 324234 sequences. (Running on oeis4.)