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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-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

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Last modified August 7 08:38 EDT 2024. Contains 375008 sequences. (Running on oeis4.)