A267012 - OEIS

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

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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