|
%I #22 Nov 05 2018 05:16:16
%S 3,5,7,13,19,23,31,37,43,53,61,73,79,83,89,103,109,113,131,137,139,
%T 157,163,173,191,193,197,199,211,223,251,257,271,277,283,293,313,317,
%U 331,337,353,359,379,383,389,397,421,443,449,457,463,467,479,499,509,521
%N Prime numbers that are not Ramanujan primes.
%C Complement of A104272 in the primes. Not the same as A059788.
%C Also known as non-Ramanujan Primes. - _John W. Nicholson_, Jan 29 2012
%H Donovan Johnson, <a href="/A174635/b174635.txt">Table of n, a(n) for n = 1..10000</a>
%H J. Sondow, <a href="http://arxiv.org/abs/0907.5232"> Ramanujan primes and Bertrand's postulate</a>, arXiv:0907.5232 [math.NT], 2009-201; Amer. Math. Monthly 116 (2009), 630-635. - _John W. Nicholson_, Jan 29 2012
%H J. Sondow, J. W. Nicholson, and T. D. Noe, <a href="http://arxiv.org/abs/1105.2249"> Ramanujan Primes: Bounds, Runs, Twins, and Gaps</a>, arXiv:1105.2249 [math.NT], 2011; J. Integer Seq. 14 (2011) Article 11.6.2 - _John W. Nicholson_, Jan 29 2012.
%t nn = 100; R = Table[0, {nn}]; s = 0;
%t Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s + 1]] = k],{k, Prime[3 nn]}
%t ];
%t R = R + 1;
%t Complement[Prime[Range[PrimePi[Last[R]]]], R] (* _Jean-François Alcover_, Nov 05 2018, after _T. D. Noe_ in A104272 *)
%o (Perl) use ntheory ":all"; my @n = grep { !is_ramanujan_prime($_) } @{primes(1e3)}; say "[@n]"; # _Dana Jacobsen_, Jul 15 2016
%o (Perl) use ntheory ":all"; my %r; $r{$_} = 1 for @{ramanujan_primes(1e7)}; say for grep { !exists $r{$_} } @{primes(1e7)}; # _Dana Jacobsen_, Jul 15 2016
%Y Cf. A104272.
%K nonn
%O 1,1
%A _T. D. Noe_, Nov 29 2010
|
