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, 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

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A260522 A260523 A260524 * A260526 A260527 A260528

Keyword

nonn,cons

Author

Robert C. Lyons and Robert G. Wilson v, Jul 28 2015

Extensions

More terms from Joerg Arndt, Aug 03 2015

Status

approved