

A092894


Decimal expansion of Frederick Magata's constant.


6



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
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OFFSET

1,1


COMMENTS

Starting with the data (1,2), (2,3), (3,5), (4,7), (5,11), (6,13), ..., (n,p_n) where p_n is the nth prime number, Frederick Magata (1998) used Newtonian interpolation to determine the coefficients b_k of a (n1) degree polynomial fit b_0 + b_1*(x1) + b_2*(x1)*(x2) + b_3*(x1)*(x2)*(x3) + ... 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

Table of n, a(n) for n=1..105.
S. R. Finch, Magata's constant.


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*k1}] [[1]], {k, 1, n1}] + Level[ P[y], {2*n2}] [[1]], 111]; RealDigits[fm][[1]] (* Steven Finch *)


CROSSREFS

Sequence in context: A110665 A063441 A319600 * A276563 A011338 A214024
Adjacent sequences: A092891 A092892 A092893 * A092895 A092896 A092897


KEYWORD

cons,nonn


AUTHOR

Robert G. Wilson v, Mar 10 2004


STATUS

approved



