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

1,2

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.

Links

Table of n, a(n) for n=1..22.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000010, A000040, A104272.

Sequence in context: A031077 A082286 A088407 * A273195 A069953 A113746

Adjacent sequences: A267009 A267010 A267011 * A267013 A267014 A267015

Keyword

nonn,more

Author

Dana Jacobsen, Jan 08 2016

Status

approved