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A260525
P(2), which is the "penalty expansion factor" needed to guarantee 2 writes of 2^k symbols on a Write Once Memory (WOM) for large k.
1
1, 2, 9, 3, 8, 1, 5, 3, 7, 3, 3, 4, 0, 4, 1, 5, 4, 9, 3, 3, 1, 6, 6, 0, 1, 6, 5, 3, 3, 0, 3, 6, 5, 7, 3, 5, 2, 1, 4, 5, 3, 6, 1, 6, 5, 4, 1, 4, 7, 4, 7, 1, 1, 4, 4, 5, 7, 0, 0, 4, 5, 5, 9, 3, 3, 9, 1, 7, 3, 3, 8, 7, 0, 0, 0, 6, 7, 6, 5, 8, 3, 3, 4, 8, 0, 9, 4, 8, 3, 1, 8, 3, 5, 0, 9, 5, 3, 4, 5, 8, 9, 9, 6, 7, 6
OFFSET
1,2
COMMENTS
An arbitrary message of n bits may be overwritten by another arbitrary message of n bits on a write-once memory using k*n bits using the Rivest-Shamir encoding. - Charles R Greathouse IV, Jul 29 2015
LINKS
Ronald L. Rivest and Adi Shamir, How to Reuse a "Write-Once" Memory, 1982
EXAMPLE
1.29381537334041549331660165330365735214536165414747114457004559339173...
MATHEMATICA
RealDigits[ 1/(1 - FindRoot[p*Log2[1/p] + (1 - p)*Log2[1/(1 - p)] + p == 1, {p, 1/4}, WorkingPrecision -> 2^7][[1, 2]]), 10, 111][[1]] (* Robert G. Wilson v, Aug 04 2015 *)
PROG
(PARI)
default(realprecision, 110);
L(x)=log(x)/log(2);
H(p)=my(q=1-p); p*L(1/p)+q*L(1/q);
t=solve(p=0.22, 0.228, H(p)-(1-p)); \\ 0.22709219521...
1/(1-t) \\ 1.29381537334041...
\\ Joerg Arndt, Aug 03 2015
CROSSREFS
Constant used in the computation of A253426.
Sequence in context: A293816 A189419 A199604 * A366249 A302973 A258403
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
More terms from Joerg Arndt, Aug 03 2015
STATUS
approved