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 A006464 Continued fraction for Sum_{n>=0} 1/4^(2^n). (Formerly M2512) 5
 0, 3, 6, 4, 4, 2, 4, 6, 4, 2, 6, 4, 2, 4, 4, 6, 4, 2, 6, 4, 4, 2, 4, 6, 2, 4, 6, 4, 2, 4, 4, 6, 4, 2, 6, 4, 4, 2, 4, 6, 4, 2, 6, 4, 2, 4, 4, 6, 2, 4, 6, 4, 4, 2, 4, 6, 2, 4, 6, 4, 2, 4, 4, 6, 4, 2, 6, 4, 4, 2, 4, 6, 4, 2, 6, 4, 2, 4, 4, 6, 4, 2, 6, 4, 4, 2, 4, 6, 2, 4, 6, 4, 2, 4, 4, 6, 2, 4, 6, 4, 4, 2, 4, 6, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n)=A004200(n) if n=0; A004200(n)+1 if n>0 (according to case u=3, b=1 of Theorem 5 (of the reference) which states that: if B(u,infinity) = Sum_{n>=0} 1/u^(2^n) = [a0, a1, a2, ...] then B(u + b,infinity) = [a0, a1+b, a2+b, a3+b,... ] (u >= 3, b >= 0)). The sum is equal to 0.316421509021893143708079...= A078585. After computing the first 10^5 terms and dropping the first two (0 & 3), only the numbers 2, 4 & 6 occur. Further I found no two 0's in a row and no three 2's or three 1's in a row. - Robert G. Wilson v, Dec 01 2002 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 Jeffrey Shallit, Simple continued fractions for some irrational numbers. J. Number Theory 11 (1979), no. 2, 209-217 [DOI] EXAMPLE 0.316421509021893143708079737... = 0 + 1/(3 + 1/(6 + 1/(4 + 1/(4 + ...)))). - Harry J. Smith, May 11 2009 MAPLE u := 4: v := 7: Buv := [u, 1, [0, u-1, u+1]]: for k from 2 to v do n := nops(Buv[3]): Buv := [u, Buv[2]+1, [seq(Buv[3][i], i=1..n-1), Buv[3][n]+1, Buv[3][n]-1, seq(Buv[3][n-i], i=1..n-2)]] od:seq(Buv[3][i], i=1..2^v); # first 2^v terms of A006464, Antonio G. Astudillo (aft_astudillo(AT)hotmail.com), Dec 02 2002 MATHEMATICA ContinuedFraction[ N[ Sum[1/4^(2^n), {n, 0, Infinity}], 1000]] PROG (PARI) { allocatemem(932245000); default(realprecision, 25000); x=suminf(n=0, 1/4^(2^n)); x=contfrac(x); for (n=1, 20001, write("b006464.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 11 2009 CROSSREFS Sequence in context: A105559 A090038 A308291 * A233825 A159354 A196500 Adjacent sequences:  A006461 A006462 A006463 * A006465 A006466 A006467 KEYWORD nonn,cofr AUTHOR EXTENSIONS Better description and more terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 19 2001 STATUS approved

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Last modified February 21 20:39 EST 2020. Contains 332111 sequences. (Running on oeis4.)