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

1,1

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.

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 *)

Prog

(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

Crossrefs

Cf. A104272.

Sequence in context: A277717 A120460 A127459 * A075579 A059788 A077171

Adjacent sequences: A174632 A174633 A174634 * A174636 A174637 A174638

Keyword

nonn

Author

T. D. Noe, Nov 29 2010

Status

approved