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%I #32 Oct 24 2019 12:13:47
%S 1,2,3,5,8,10,14,20,25,28,35,64,72,92,136,160,187,213,299,316,364,454,
%T 694,923,1497,3778,4766,6710,18860,44556,73998,82553,87762,95249,
%U 354770,415588,420892,1115579,8546951
%N Consider the nontrivial zeros of the Riemann zeta function on the critical line 1/2 + i*t and the gap, or first difference, between two consecutive such zeros; a(n) is the lesser of the two zeros at a place where the gap attains a new minimum.
%C Since all zeros are assumed to be on the critical line, the gap, or first difference, between two consecutive zeros is measured as the difference between the two imaginary parts.
%C Inspired by A002410.
%C No other terms < 10000000. The minimum gap so far is 0.002323...
%H Glen Pugh, <a href="https://web.viu.ca/pughg/RiemannZeta/RiemannZetaLong.html">The Riemann Hypothesis in a Nutshell</a>.
%F a(n) = A326502(n) + 1. - _Artur Jasinski_, Oct 24 2019
%e a(1)=1 since the first Riemann zeta zero, 1/2 + i*14.13472514... (A058303) has no previous zero, so its gap is measured from 0.
%e a(2)=2 since the second Riemann zeta zero, 1/2 + i*21.02203964... (A065434) has a gap of 6.887314497... which is less than the previous gap of ~14.13472514.
%e a(3)=3 since the third Riemann zeta zero, 1/2 + i*25.01085758... (A065452) has a gap of 3.988817941... which is less than ~6.887314497.
%e The fourth Riemann Zeta zero, 1/2 + i*30.42487613... (A065453) has a gap of 5.414018546... which is not less than ~6.887314497 and therefore is not in the sequence.
%e a(4)=5 since the fifth Riemann zeta zero, 1/2 + i*32.93506159... (A192492) has a gap of 2.510185462... which is less than ~3.988817941.
%e a(5)=8 since the eighth Riemann zeta zero, 1/2 + i*43.32707328... has a gap of 2.408354269... which is less than ~2.510185462.
%t k = 1; mn = Infinity; y = 0; lst = {}; While[k < 10001, z = N[ Im@ ZetaZero@ k, 64]; If[z - y < mn, mn = z - y; AppendTo[lst, k]]; y = z; k++]; lst
%Y Cf. A002410, A100060, A161914, A117538, A153595, A326502.
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Jan 27 2015
%E a(38) from _Arkadiusz Wesolowski_, Nov 08 2015
%E a(39) from _Artur Jasinski_, Oct 24 2019