A066277 Primes p(m) such that a prime number q exists so that p(m)-q = c(m), the m-th composite number.

2, 3, 5, 7, 17, 23, 29, 31, 41, 43, 67, 89, 97, 131, 139, 157, 281, 311, 313, 331, 353, 379, 401, 431, 449, 499, 569, 571, 607, 631, 683, 733, 743, 751, 787, 829, 881, 883, 947, 967, 983, 1033, 1091, 1117, 1123, 1151, 1301, 1303, 1327, 1373, 1543, 1559

Offset: 1

Author

Labos Elemer, Dec 10 2001

Keywords

• nonn

Comments

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

Examples

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

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A002808, A038529, A060253.

Programs

Mathematica

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 *)

Formula

a(n) = prime(A060253(n)) or A000040(A060253(n)). - Michel Marcus, Dec 11 2017