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 A239199 Expansion of Pi in the irrational base b=sqrt(3). 3
 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET -2 COMMENTS The negative offset is chosen as to have Pi = sum(a(i)*b^-i, i=offset...+oo), with the base b=sqrt(3), cf. Example. Sqrt(3) is the largest base of the form sqrt(n) < 2, such that the expansion of any number in this base has only digits 1 and 0 (which allows a condensed version of the expansion which lists only the positions of the nonzero digits, here: -2, 4, 7, 9, 12, 14, 17, 18, 24, 26, ...). Log(7) has this maximal property for bases of the form log(n). LINKS George Bergman, A number system with an irrational base, Math. Mag. 31 (1957), pp. 98-110. EXAMPLE Pi = sqrt(3)^2 + sqrt(3)^-4 + sqrt(3)^-7 + ... = [1,0,0;0,0,0,1,0,0,1,...]_{sqrt(3)}. MATHEMATICA RealDigits[Pi, Sqrt[3], 105][[1]] (* T. D. Noe, Mar 12 2014 *) PROG (PARI) base(x, b=sqrt(3), L=99/*max.# digits for fract.part*/, a=[])={ forstep(k=log(x)\log(b), -L, -1, a=concat(a, d=x\b^k); (x-=d*b^k)||k>0||break); a} A239199 = base(Pi) \\ defines A239199 as a vector; indices are here 1, 2, 3... instead of -2, -1, 0, .... CROSSREFS Cf. A238897 (Pi in base sqrt(2)), A050948 (Pi in base e), A050949 (e in base Pi), A102243 (Pi in the golden base). Sequence in context: A089010 A162289 A122276 * A265718 A267463 A264442 Adjacent sequences:  A239196 A239197 A239198 * A239200 A239201 A239202 KEYWORD nonn,base AUTHOR M. F. Hasler, Mar 12 2014 STATUS approved

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)