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 A059095 List consisting of the representation of n in base 3 using digits -1, 0, 1. 27
 1, 1, -1, 1, 0, 1, 1, 1, -1, -1, 1, -1, 0, 1, -1, 1, 1, 0, -1, 1, 0, 0, 1, 0, 1, 1, 1, -1, 1, 1, 0, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 0, 1, -1, -1, 1, 1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, 1, 1, -1, 1, -1, 1, -1, 1, 0, 1, -1, 1, 1, 1, 0, -1, -1, 1, 0, -1, 0, 1, 0, -1, 1, 1, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, -1, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS Every natural number n has a unique representation as n = Sum_{i=1..k} e(i)*(3^i) for some k where e(i) is one of -1,0,1. Example: 25 = 27-3+1 = 1*3^3+0*3^2+(-1)*3^1+1*3^0 so its representation is 1,0,-1,1. So by writing n in this base 3 representation and juxtaposing we get the sequence: (1), (1,-1), (1,0), (1,1), (1,-1,-1), ... REFERENCES D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..4560 (rows 1 <= n <= 729 = 3^6, flattened) Wikipedia, Balanced Ternary FORMULA n = Sum_{0 <= k < A134021(n)} a(A134421(n)-2-k)*3^k, for n>0. - Reinhard Zumkeller, Oct 25 2007 EXAMPLE From Michael De Vlieger, Jun 27 2020: (Begin) First 27 rows, with terms aligned with powers of 3: 3^3 3^2 3^1 3^0 -------------------- 1: 1; 2: 1, -1; 3: 1, 0; 4: 1, 1; 5: 1, -1, -1; 6: 1, -1, 0; 7: 1, -1, 1; 8: 1, 0, -1; 9: 1, 0, 0; 10: 1, 0, 1; 11: 1, 1, -1; 12: 1, 1, 0; 13: 1, 1, 1; 14: 1, -1, -1, -1; 15: 1, -1, -1, 0; 16: 1, -1, -1, 1; 17: 1, -1, 0, -1; 18: 1, -1, 0, 0; 19: 1, -1, 0, 1; 20: 1, -1, 1, -1; 21: 1, -1, 1, 0; 22: 1, -1, 1, 1; 23: 1, 0, -1, -1; 24: 1, 0, -1, 0; 25: 1, 0, -1, 1; 26: 1, 0, 0, -1; 27: 1, 0, 0, 0; ... (End) MATHEMATICA Array[If[First@ # == 0, Rest@ #, #] &[Prepend[IntegerDigits[#, 3], 0] //. {a___, b_, 2, c___} :> {a, b + 1, -1, c}] &, 32] // Flatten (* Michael De Vlieger, Jun 27 2020 *) PROG (Python) def b3(n): if n == 0: return [] carry, trailing = [(0, 0), (0, 1), (1, -1)][n % 3] return b3(n//3 + carry) + [trailing] t = [] for n in range(50): t += b3(n) print(t) # Andrey Zabolotskiy, Nov 10 2019 (PARI) row(n) = apply(d->d-1, digits(n + 3^(logint(n<<1, 3)+1)>>1, 3)); \\ Kevin Ryde, Mar 04 2022 CROSSREFS Cf. A117966, A134021 (row lengths, starting from row 1), A102283 (last each row), A065363 (row sums). Cf. A003137 (ternary). Sequence in context: A099990 A089939 A330550 * A187944 A105597 A188470 Adjacent sequences: A059092 A059093 A059094 * A059096 A059097 A059098 KEYWORD tabf,sign,easy AUTHOR Avi Peretz (njk(AT)netvision.net.il), Feb 13 2001 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Jul 20 2001 Offset corrected by Andrey Zabolotskiy, Nov 10 2019 STATUS approved

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Last modified July 25 11:18 EDT 2024. Contains 374588 sequences. (Running on oeis4.)