1,2

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

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

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.

A. Brousseau, Number Theory Tables. Fibonacci Association, San Jose, CA, 1973, p. 159.

K. R. Bhutani and A. B. Levin, "The Problem of Sawing a Chain", Journal of Recreational Mathematics 2002-3 31(1) 32-35.

G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.

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.

T. D. Noe, Table of n, a(n) for n=1..300

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.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Ray Ballinger, Woodall Primes: Definition and Status

C. K. Caldwell, Woodall Numbers

Paul Leyland, Factors of Cullen and Woodall numbers

Paul Leyland, Generalized Cullen and Woodall numbers

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

T. Sillke, Using Chains Links To Pay For A Room

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Wikipedia, Woodall number

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

A003261:=(-1-2*z+4*z**2)/(z-1)/(-1+2*z)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]

Cf. A002234, A002064, A005849, A050918.

a(n) = A036289(n)-1 = A002064(n)-2.

Cf. A133653.

Sequence in context: A077037 A104149 A001275 this_sequence A066187 A114246 A048457

Adjacent sequences: A003258 A003259 A003260 this_sequence A003262 A003263 A003264

nonn,easy,nice

njas