A064402 - OEIS

%I #25 Sep 08 2022 08:45:04

%S 1,2,4,6,18,22,24,26,32,34,42,48,66,70,72,82,92,96,98,100,102,104,106,

%T 108,114,116,126,130,144,150,152,158,172,180,200,202,204,206,218,222,

%U 228,236,270,282,290,300,312,322,324,328,330,350,352,356,362,378,384

%N Numbers n such that prime(n)+n is a prime, where prime(n) denotes the n-th prime number.

%C a(n) = order among the primes of A061067(n).

%C Except for the first one all terms are even. Conjecture: First differences include all even integers. - _Zak Seidov_, Nov 10 2013

%H Harry J. Smith, <a href="/A064402/b064402.txt">Table of n, a(n) for n=1..1000</a>

%F a(n) = A061068(n) - A061067(n-1).

%F A014688(a(n)) = A061068(n). - _Zak Seidov_, Nov 10 2013

%t Select[ Range[ 400 ], PrimeQ[ Prime[ # ] + # ] & ]

%o (PARI) { n=0; for (m=1, 10^9, if (isprime(prime(m) + m), write("b064402.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Sep 13 2009

%o (Magma) [n: n in [0..500]| IsPrime(NthPrime(n) +n)]; // _Vincenzo Librandi_, Apr 06 2011

%Y Cf. A061067, A061068, A064269.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 28 2001

%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 08 2007