cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A197185 The Riemann primes of the psi type and index 1.

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%I A197185 #24 Dec 03 2018 12:56:34
%S A197185 2,59,73,97,109,113,199,283,463,467,661,1103,1109,1123,1129,1321,1327,
%T A197185 1423,2657,2803,2861,3299,5381,5881,6373,6379,9859,9931,9949,10337,
%U A197185 10343,11777,19181,19207,19373,24107,24109,24113,24121,24137,42751,42793,42797
%N A197185 The Riemann primes of the psi type and index 1.
%C A197185 The sequence consists of the prime numbers p that are champions (left to right maxima) of the function |psi(p)-p|, where psi(p) is the Chebyshev psi function.
%H A197185 Dana Jacobsen, <a href="/A197185/b197185.txt">Table of n, a(n) for n = 1..583</a>
%H A197185 M. Planat and P. Solé, <a href="http://arxiv.org/abs/1109.6489">Efficient prime counting and the Chebyshev primes</a> arXiv:1109.6489 [math.NT], 2011.
%H A197185 L. Schoenfeld, <a href="http://dx.doi.org/10.1090/S0025-5718-1976-0457374-X">Sharper bounds for the Chebyshev functions theta(x) and psi(x). II</a>, Math. Comp. 30 (1975) 337-360.
%t A197185 ChebyshevPsi[n_] := Range[n] // MangoldtLambda // Total;
%t A197185 Reap[For[max=0; p=2, p<50000, p = NextPrime[p], f = Abs[ChebyshevPsi[p]-p]; If[f > max, max = f; Print[p]; Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Dec 03 2018 *)
%o A197185 (Perl) use ntheory ":all"; my($max,$f)=(0); forprimes { $f=abs(chebyshev_psi($_)-$_); if ($f > $max) { say; $max=$f; } } 10000; # _Dana Jacobsen_, Dec 29 2015
%Y A197185 Cf. A196667, A197186, A197187, A197188.
%K A197185 nonn
%O A197185 1,1
%A A197185 _Michel Planat_, Oct 11 2011