|
Search: id:A092894
|
|
|
| A092894 |
|
Decimal expansion of Frederick Magata's constant. |
|
+0
7
|
|
| 3, 4, 0, 7, 0, 6, 9, 1, 6, 5, 6, 2, 7, 2, 5, 6, 1, 4, 2, 2, 1, 9, 4, 5, 8, 2, 6, 2, 8, 2, 7, 1, 8, 0, 6, 5, 3, 5, 5, 4, 0, 3, 4, 4, 3, 8, 0, 1, 5, 0, 3, 2, 1, 1, 6, 1, 9, 1, 0, 3, 3, 8, 2, 7, 5, 7, 2, 9, 6, 9, 9, 3, 8, 7, 0, 4, 1, 0, 3, 5, 1, 4, 3, 0, 0, 9, 9, 0, 0, 4, 0, 9, 3, 8, 9, 4, 7, 4, 1, 0, 8, 7, 8, 7, 1
(list; cons; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Starting with the data (1,2), (2,3), (3,5), (4,7), (5,11), (6,13), ..., (n,p_n) where p_n is the n-th prime number, Frederick Magata (1998) used Newtonian interpolation to determine the coefficients b_k of a (n-1) degree polynomial fit b_0 + b_1*(x-1) + b_2*(x-1)*(x-2) + b_3*(x-1)*(x-2)*(x-3) + ... The sum of all the coefficients b_k, for arbitrarily large n, appears to converge to 3.407069...
Although it takes only 86 terms to secure the decimal representation above, Robert G. Wilson v took it out to 1000 terms.
|
|
LINKS
|
S. R. Finch, from Simon Plouffe's Inverter.
|
|
EXAMPLE
|
FM = 3.407069165627256142219458262827180653554034438015032116191033...
|
|
MATHEMATICA
|
n := 100; P[y_] := P[y] = InterpolatingPolynomial[ Array[ Prime, n], x] /. x->y; fm = N[ Sum[ Level[ P[y], {2*k-1}] [[1]], {k, 1, n-1}] + Level[ P[y], {2*n-2}] [[1]], 111]; RealDigits[fm][[1]] (from S. R. Finch (Steven.Finch(AT)inria.fr))
|
|
CROSSREFS
|
Sequence in context: A105826 A110665 A063441 this_sequence A011338 A049251 A158674
Adjacent sequences: A092891 A092892 A092893 this_sequence A092895 A092896 A092897
|
|
KEYWORD
|
cons,nonn
|
|
AUTHOR
|
Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 10 2004
|
|
|
Search completed in 0.002 seconds
|
