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A239200
Expansion of Pi in the irrational base b=log(7).
0
1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1
OFFSET
-1
COMMENTS
The negative offset is chosen as to have Pi = sum(a(i)*b^-i, i=offset...+oo), with the base b=log(7), cf. Example.
Log(7) is the largest base of the form log(n) < 2, such that the expansion has only digits 1 and 0 (and can therefore also be recorded in a condensed way by just listing the positions of nonzero digits, cf. example). Sqrt(3) has this maximal property for bases of the form sqrt(n).
LINKS
George Bergman, A number system with an irrational base, Math. Mag. 31 (1957), pp. 98-110 (available on JSTOR.org).
EXAMPLE
Pi = log(7)^1 + log(7)^0 + log(7)^-3 + log(7)^-5 + ... = [1,1;0,0,1,0,1,1,...]_{log(7)}, which could also be encoded as (1,0,-3,-5,...) or (-1,0,3,5,...) (sequence of which the present one is the characteristic function).
PROG
(PARI) base(x, b=log(7), L=99, a=[])={ forstep(k=log(x)\log(b), -L, -1, a=concat(a, d=x\b^k); (x-=d*b^k)||k>0||break); a}
base(Pi) \\ returns this sequence as a vector (whose components are indexed by 1, 2, 3... instead of -1, 0, 1, ...).
CROSSREFS
Cf. A238897 (Pi in base sqrt(2)), A239199 (Pi in base sqrt(3)), A050948 (Pi in base e), A050949 (e in base Pi), A102243 (Pi in the golden base).
Sequence in context: A328102 A177444 A325896 * A157686 A181115 A284527
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Mar 12 2014
STATUS
approved