A319953 -id:A319953 - cp's OEIS frontend

A319954 Infinite word over {0,1,2} formed from list of binary words of lengths 0, 1, 2, etc., including empty word, each prefixed by a 2.

2, 2, 0, 2, 1, 2, 0, 0, 2, 0, 1, 2, 1, 0, 2, 1, 1, 2, 0, 0, 0, 2, 0, 0, 1, 2, 0, 1, 0, 2, 0, 1, 1, 2, 1, 0, 0, 2, 1, 0, 1, 2, 1, 1, 0, 2, 1, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 1, 0, 2, 0, 0, 1, 1, 2, 0, 1, 0, 0, 2, 0, 1, 0, 1, 2, 0, 1, 1, 0, 2, 0, 1

Offset: 0

N. J. A. Sloane, Oct 04 2018

			The word written without commas:
220212002012102112000200120102011210021012110211120000200012001020011...

Rémy Sigrist, Table of n, a(n) for n = 0..25000
Carl Pomerance, John Michael Robson, and Jeffrey Shallit, Automaticity II: Descriptional complexity in the unary case, Theoretical computer science 180.1-2 (1997): 181-201.

Cf. A001855, A030302, A214339, A319953.

k=0; for (n=0, oo, b=binary(n+1); b[1]++; for (i=1, #b, print1 (b[i] ", "); if (k++==87, quit))) \\ Rémy Sigrist, Oct 04 2018

a(n) = A030302(n+1) + [n belongs to A001855] (where [] is an Iverson bracket). - Rémy Sigrist, Oct 04 2018

Data corrected and extended by Rémy Sigrist, Oct 04 2018

A346524 Write n in ternary, replace each 2 with -1, interpret each "-" as a subtraction operator, and evaluate the resulting expression in ternary.

Original entry on oeis.org

0, 1, -1, 3, 4, 0, -3, -4, -2, 9, 10, 2, 12, 13, 3, -2, -3, -1, -9, -10, -4, -12, -13, -5, -4, -5, -3, 27, 28, 8, 30, 31, 9, 0, -1, 1, 36, 37, 11, 39, 40, 12, 1, 0, 2, -8, -9, -3, -11, -12, -4, -3, -4, -2, -27, -28, -10, -30, -31, -11, -6, -7, -5, -36, -37

Offset: 0

Johnathan Abdoo, Jul 21 2021

Instead of interpreting the -1 as done in balanced ternary (as in A117966), read the newly formed string as a mathematical expression and evaluate it in ternary as if each "-" is a subtraction operator.
Those n which do not contain a 2 in ternary (A005836) remain unchanged and are record highs.
Those n which in ternary are a binary number prefixed by a 2 (A319953) give the record lows.

			For n = 208893 = 101121112210_3, changing each 2 to a -1 gives 1011-1111-1-110; interpreting each "-" as a subtraction operator gives 1011_3 - 1111_3 - 1_3 - 110_3 = 31 - 40 - 1 - 12 = -22, so a(208893) = -22.
For n = 25 = 221_3, changing the 2's to (-1)'s gives -1-11; interpreting the leading "-" as a unary minus (so the expression starts with a negative 1) and the remaining "-" as a subtraction operator gives -1_3 - 11_3 = -1 - 4 = -5, so a(25) = -5.

Cf. A005836 (fixed points), A319953.

Cf. A117966.

a(n) = my(v=digits(n,3),lo=#v,ret=0); forstep(i=#v,1,-1, if(v[i]==2, v[i]=1; ret -= fromdigits(v[i..lo],3); lo=i-1)); ret + fromdigits(v[1..lo],3); \\ Kevin Ryde, Jul 23 2021

cp's OEIS Frontend

A319954 Infinite word over {0,1,2} formed from list of binary words of lengths 0, 1, 2, etc., including empty word, each prefixed by a 2.

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