A000709 Related to population of numbers of form x^2 + y^2. (Formerly M1060 N0398)

1, 2, 4, 7, 12, 21, 38, 68, 124, 229, 428, 806, 1530, 2919, 5591, 10750, 20730, 40077, 77653, 150752, 293161, 570963, 1113524, 2174315, 4250367, 8317036, 16289636, 31931697, 62642861, 122980015, 241595101, 474910732, 934088141, 1838227618, 3619356631

Offset

1,2

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Daniel Shanks, The second-order term in the asymptotic expansion of B(x), Mathematics of Computation 18 (1964), pp. 75-86.

Index entries for sequences related to populations of quadratic forms

Formula

a(n) = Integral_{u=1..2^(n-1)} 1/sqrt(log(u)) du. - Based on Alois P. Heinz's Maple program, Alonso del Arte, Oct 24 2014

Maple

Digits := 500:
a:= n-> `if`(n=1, 1, round(evalf(int(1/sqrt(ln(u)), u=1..2^(n-1))))):
seq(a(n), n=1..35); # Alois P. Heinz, Dec 26 2010

Mathematica

Table[Floor[Integrate[1/Sqrt[Log[u]], {u, 1, 2^(n - 1)}]], {n, 2, 40}] (* Based on Alois P. Heinz's Maple program, Alonso del Arte, Oct 24 2014 *)

Crossrefs

Sequence in context: A307058 A307060 A218600 * A054161 A023433 A190168

Adjacent sequences: A000706 A000707 A000708 * A000710 A000711 A000712

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(17) corrected and more terms from Alois P. Heinz, Dec 26 2010

Status

approved