A066277 - OEIS

A066277

Primes p(m) such that a prime number q exists so that p(m)-q = c(m), the m-th composite number.

%I #25 Dec 12 2017 03:44:36

%S 2,3,5,7,17,23,29,31,41,43,67,89,97,131,139,157,281,311,313,331,353,

%T 379,401,431,449,499,569,571,607,631,683,733,743,751,787,829,881,883,

%U 947,967,983,1033,1091,1117,1123,1151,1301,1303,1327,1373,1543,1559

%N Primes p(m) such that a prime number q exists so that p(m)-q = c(m), the m-th composite number.

%C Number of terms < 10^k: 4, 13, 41, 177, 1119, 6963, 48647, 359109, 2766164, ..., . - _Robert G. Wilson v_, Dec 11 2017

%H Robert G. Wilson v, <a href="/A066277/b066277.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = prime(A060253(n)) or A000040(A060253(n)). - _Michel Marcus_, Dec 11 2017

%e p(25) = A000040(25) = 97; 97 - 61 = A002808(25) = c(25) = 38 and 61 is prime.

%t Composite[n_Integer] := FixedPoint[n + PrimePi@# +1 &, n + PrimePi@n +1]; fQ[n_] := PrimeQ[Prime@n - Composite@n]; Prime@ Select[ Range@250, fQ] (* _Robert G. Wilson v_, Dec 11 2017 *)

%Y Cf. A000040, A002808, A038529, A060253.

%K nonn

%O 1,1

%A _Labos Elemer_, Dec 10 2001