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A000134
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Positive zeros of Bessel function of order 0 rounded to nearest integer.
(Formerly M1570 N0613)
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2
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2, 6, 9, 12, 15, 18, 21, 24, 27, 31, 34, 37, 40, 43, 46, 49, 53, 56, 59, 62, 65, 68, 71, 75, 78, 81, 84, 87, 90, 93, 97, 100, 103, 106, 109, 112, 115, 119, 122, 125, 128, 131, 134, 137, 141, 144, 147, 150, 153, 156, 159, 163, 166, 169, 172, 175, 178, 181, 185, 188
(list;
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OFFSET
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1,1
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 409.
British Association Mathematical Tables, Vol. 6, Bessel Functions, Part 1, Functions of Order Zero and Unity. Cambridge Univ. Press, 1937, p. 171.
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).
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LINKS
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David W. Wilson, Table of n, a(n) for n = 1..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for sequences related to Bessel functions or polynomials
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FORMULA
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a(n) = Pi*n + O(1). Probably a(n+1) - a(n) is 3 or 4 for all n. - Charles R Greathouse IV, Oct 04 2016
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MATHEMATICA
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Table[BesselJZero[0, n] // Round, {n, 1, 40}] (* Jean-François Alcover, Feb 04 2016 *)
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PROG
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(PARI) a(n)=if(n<1, 0, n=a(n-1); until(besselj(0, n-1/2)*besselj(0, n+1/2)<0, n++); n)
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CROSSREFS
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Sequence in context: A287445 A119720 A173978 * A120701 A350235 A189752
Adjacent sequences: A000131 A000132 A000133 * A000135 A000136 A000137
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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