%I A003261 M4379
%S A003261 1,7,23,63,159,383,895,2047,4607,10239,22527,49151,106495,229375,
%T A003261 491519,1048575,2228223,4718591,9961471,20971519,44040191,92274687,
%U A003261 192937983,402653183,838860799,1744830463,3623878655,7516192767
%N A003261 Woodall (or Riesel) numbers: n*2^n - 1.
%C A003261 For n>1, a(n) is base at which zero is reached for the function "write 
               f(j) in base j, read as base j+1 and then subtract 1 to give f(j+1)" 
               starting from f(n)=n^2-1 - Henry Bottomley (se16(AT)btinternet.com), 
               Aug 06 2000
%C A003261 Sequence corresponds also to the maximum chain length of the classic 
               puzzle whereby, under agreed commercial terms, an asset of unringed 
               golden chain, when judiciously fragmented into as few as n pieces 
               and n-1 opened links (through n-1 cuts), might be used to settle 
               debt sequentially, with a golden link covering for unit cost. Here 
               beside the n-1 opened links, the n fragmented pieces have lengths 
               n, 2*n, 4*n, ..., 2^(n-1)*n. For instance, the chain of original 
               length a(5)=159, if segregated by 4 cuts into 5+1+10+1+20+1+40+1+80, 
               may be used to pay sequentially, i.e. a link-cost at a time, for 
               an equivalent cost up to 159 links, to the same creditor. - Lekraj 
               Beedassy (blekraj(AT)yahoo.com), Feb 06 2003
%D A003261 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003261 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A003261 A. Brousseau, Number Theory Tables. Fibonacci Association, San Jose, 
               CA, 1973, p. 159.
%D A003261 K. R. Bhutani and A. B. Levin, "The Problem of Sawing a Chain", Journal 
               of Recreational Mathematics 2002-3 31(1) 32-35.
%D A003261 G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence 
               Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%D A003261 M. Gardner, Martin Gardner's Sixth Book of Mathematical Diversions from 
               Scientific American, "Gold Links", Problem 4, pp. 50-51; 57-58, University 
               of Chicago Press, 1983.
%H A003261 T. D. Noe, <a href="b003261.txt">Table of n, a(n) for n=1..300</a>
%H A003261 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A003261 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A003261 Ray Ballinger, <a href="http://www.prothsearch.net/woodall.html">Woodall 
               Primes: Definition and Status</a>
%H A003261 C. K. Caldwell, <a href="http://primes.utm.edu/glossary/page.php?sort=WoodallNumber">
               Woodall Numbers</a>
%H A003261 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/
               cullen_woodall/cw.htm">Factors of Cullen and Woodall numbers</a>
%H A003261 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/
               cullen_woodall/gcw.htm">Generalized Cullen and Woodall numbers</a>
%H A003261 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha122.htm">Factorizations of many number sequences</a>
%H A003261 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha123.htm">Factorizations of many number sequences</a>
%H A003261 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha124.htm">Factorizations of many number sequences</a>
%H A003261 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha125.htm">Factorizations of many number sequences</a>
%H A003261 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha103.htm">Factorizations of many number sequences</a>
%H A003261 T. Sillke, <a href="http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/
               chain-link-pay">Using Chains Links To Pay For A Room</a>
%H A003261 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               WoodallNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A003261 Wikipedia, <a href="http://en.wikipedia.org/wiki/Woodall_number">Woodall 
               number</a>
%F A003261 Binomial transform of A133653 and double binomial transform of [1, 5, 
               -1, 1, -1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 
               19 2007
%p A003261 A003261:=(-1-2*z+4*z**2)/(z-1)/(-1+2*z)**2; [Conjectured by S. Plouffe 
               in his 1992 dissertation.]
%Y A003261 Cf. A002234, A002064, A005849, A050918.
%Y A003261 a(n) = A036289(n)-1 = A002064(n)-2.
%Y A003261 Cf. A133653.
%Y A003261 Sequence in context: A077037 A104149 A001275 this_sequence A066187 A114246 
               A048457
%Y A003261 Adjacent sequences: A003258 A003259 A003260 this_sequence A003262 A003263 
               A003264
%K A003261 nonn,easy,nice
%O A003261 1,2
%A A003261 N. J. A. Sloane (njas(AT)research.att.com).