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A000134 Positive zeros of Bessel function of order 0 rounded to nearest integer.
(Formerly M1570 N0613)

%I M1570 N0613

%S 2,6,9,12,15,18,21,24,27,31,34,37,40,43,46,49,53,56,59,62,65,68,71,75,

%T 78,81,84,87,90,93,97,100,103,106,109,112,115,119,122,125,128,131,134,

%U 137,141,144,147,150,153,156,159,163,166,169,172,175,178,181,185,188

%N Positive zeros of Bessel function of order 0 rounded to nearest integer.

%D 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.

%D British Association Mathematical Tables, Vol. 6, Bessel Functions, Part 1, Functions of Order Zero and Unity. Cambridge Univ. Press, 1937, p. 171.

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

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

%H David W. Wilson, <a href="/A000134/b000134.txt">Table of n, a(n) for n = 1..1000</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>

%F 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

%t Table[BesselJZero[0, n] // Round, {n, 1, 40}] (* _Jean-Fran├žois Alcover_, Feb 04 2016 *)

%o (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)

%K nonn

%O 1,1

%A _N. J. A. Sloane_

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Last modified November 13 15:41 EST 2019. Contains 329106 sequences. (Running on oeis4.)