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A174635 Prime numbers that are not Ramanujan primes. 8
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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,changed

AUTHOR

T. D. Noe, Nov 29 2010

STATUS

approved

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Last modified November 15 09:36 EST 2018. Contains 317232 sequences. (Running on oeis4.)