A174635 Prime numbers that are not Ramanujan primes.

3, 5, 7, 13, 19, 23, 31, 37, 43, 53, 61, 73, 79, 83, 89, 103, 109, 113, 131, 137, 139, 157, 163, 173, 191, 193, 197, 199, 211, 223, 251, 257, 271, 277, 283, 293, 313, 317, 331, 337, 353, 359, 379, 383, 389, 397, 421, 443, 449, 457, 463, 467, 479, 499, 509, 521

Offset: 1

Author

T. D. Noe, Nov 29 2010

Keywords

• nonn

Comments

Complement of A104272 in the primes. Not the same as A059788.

Also known as non-Ramanujan Primes. - John W. Nicholson, Jan 29 2012

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000
• J. Sondow, Ramanujan primes and Bertrand's postulate, arXiv:0907.5232 [math.NT], 2009-201; Amer. Math. Monthly 116 (2009), 630-635. - _John W. Nicholson_, Jan 29 2012
• J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, arXiv:1105.2249 [math.NT], 2011; J. Integer Seq. 14 (2011) Article 11.6.2 - _John W. Nicholson_, Jan 29 2012.

Crossrefs

Cf. A104272.

Programs

Mathematica

nn = 100; R = Table[0, {nn}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s + 1]] = k],{k, Prime[3 nn]}
];
R = R + 1;
Complement[Prime[Range[PrimePi[Last[R]]]], R] (* Jean-François Alcover, Nov 05 2018, after T. D. Noe in A104272 *)

Perl

use ntheory ":all";  my @n = grep { !is_ramanujan_prime($) } @{primes(1e3)}; say "[@n]"; # _Dana Jacobsen, Jul 15 2016

Perl

use ntheory ":all"; my %r; $r{$} = 1 for @{ramanujan_primes(1e7)}; say for grep { !exists $r{$} } @{primes(1e7)}; # Dana Jacobsen, Jul 15 2016