A049078 Primes prime(k) for which A049076(k) = 2.

3, 17, 41, 67, 83, 109, 157, 191, 211, 241, 283, 353, 367, 401, 461, 509, 547, 563, 587, 617, 739, 773, 797, 859, 877, 967, 991, 1031, 1087, 1171, 1201, 1217, 1409, 1433, 1447, 1471, 1499, 1597, 1621, 1669, 1723, 1741, 1823, 1913, 2027, 2063, 2081, 2099

Offset: 1

Author

Neil Fernandez

Keywords

• nonn

Examples

			For these primes S(p) is a prime but S(S(p)) is not. E.g. S(17)=7, S(7)=4.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• N. Fernandez, An order of primeness, F(p)
• N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Crossrefs

Cf. A049076, A007821, A049079-A049081, A058322, A058324-A058328, A093046, A006450, A018252, A236542.

Let A = primes A000040, B = nonprimes A018252. The 2-level compounds are AA = A006450, AB = A007821, BA = A078782, BB = A102615. The 3-level compounds AAA, AAB, ..., BBB are A038580, A049078, A270792, A102617, A270794, A270795, A270796, A102616.

Programs

Maple

A049078 := proc(n) ithprime(A007821(n)) ; end proc: # R. J. Mathar, Aug 14 2008

Mathematica

Nest[ Prime, Select[ Range[70], !PrimeQ[ # ] &], 2] (* Robert G. Wilson v, Mar 15 2004 *)

PARI

is(n)=my(p=primepi(n)); isprime(p) && !isprime(primepi(p)) && isprime(n) \\ Charles R Greathouse IV, Apr 29 2015

Formula

a(n) = prime(A007821(n)). - Juri-Stepan Gerasimov, Aug 11 2008

a(n) ~ A006450(n) ~ n log^2 n. - Charles R Greathouse IV, Apr 29 2015

Extensions

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar

Spelling/notation corrections by Charles R Greathouse IV, Mar 18 2010