A267012 Numbers n such that the n-th prime equals the n-th Ramanujan prime of the totient of n.

1, 10, 28, 50, 56, 874, 1575, 3604, 4966, 30704, 55964, 56372, 145616, 195016, 200792, 227278, 1679518, 2611874, 3028502, 23070602, 27365684, 45639626

Offset: 1

Author

Dana Jacobsen, Jan 08 2016

Keywords

• nonn
• more

Comments

n such that A000040(n) = A104272(A000010(n)).

Values are not prime, since for n > 1, A104272(n) > 2 * A000040(n) and A000010(n) = n-1 for prime n.

Examples

			28 is in the sequence because the totient of 28 is 12, the 12th Ramanujan prime is 107, and the 28th prime is also 107.
		

Crossrefs

Cf. A000010, A000040, A104272.

Programs

Mathematica

lim = 60000; r = Table[0, {lim}]; s = 0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < lim, r[[s + 1]] = k], {k, Prime[3 lim]}]; r = r + 1; Select[Range@ lim, Prime@ # == r[[EulerPhi@ #]] &] (* Michael De Vlieger, Jan 09 2016, after T. D. Noe at A104272 *)

Perl

use ntheory ":all"; sub is { my $n = shift; nth_prime($n) == nth_ramanujan_prime(euler_phi($n)); } for (1..1e5) { say if is($_) }

Perl

use ntheory ":all"; my $lim = 1e7; my($pr,$rp) = (primes(nth_prime($lim)), ramanujan_primes(nth_ramanujan_prime($lim))); for (1..$lim) { say if $pr->[$-1] == $rp->[euler_phi($)-1]; } # high memory use but faster