|
|
A368497
|
|
Decimal expansion of the fixed point c = S(c) of S(x) = Sum_{k>=1} (prime(k) - x) / Product_{i=1..k-1} prime(i).
|
|
0
|
|
|
1, 7, 0, 9, 7, 5, 5, 1, 2, 4, 4, 7, 5, 9, 3, 1, 3, 0, 1, 2, 6, 8, 2, 5, 9, 0, 7, 0, 0, 9, 0, 8, 0, 9, 4, 2, 1, 8, 2, 5, 9, 9, 9, 6, 8, 9, 0, 7, 7, 1, 5, 5, 8, 2, 7, 6, 5, 7, 3, 2, 5, 1, 1, 2, 8, 6, 3, 2, 1, 3, 6, 4, 9, 5, 6, 4, 4, 3, 3, 6, 7, 9, 1, 3, 2, 2, 7, 4, 6, 6, 2, 7, 5, 2, 4, 5, 6, 4, 0, 7, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
S(x) = (1-x)*(1+A064648) + A249270 is linear so the fixed point is unique.
With this constant as h(1) = c, sequence h(n+1) = ceiling(h(n)) * (h(n) - ceiling(h(n)) + c) is real numbers with the property that ceiling(h(n)) = prime(n).
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
1.709755124475931301268259070090809...
|
|
PROG
|
(PARI) solve(x=1, 2, suminf(k=1, (prime(k)-x)/prod(i=1, k-1, prime(i)))-x) \\ Michal Paulovic, Dec 28 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|