A049203 Primes for which A049076(p) >= 5.

31, 127, 709, 1787, 5381, 8527, 15299, 19577, 27457, 42043, 52711, 72727, 87803, 96797, 112129, 137077, 167449, 173867, 219613, 239489, 250751, 285191, 318211, 352007, 401519, 443419, 464939, 490643, 506683, 527623, 648391, 683873, 718807

Offset: 1

Author

Neil Fernandez

Keywords

• nonn

Comments

Union of A049081, A058322, A058324-A058328, A093046, etc. - R. J. Mathar, Jul 07 2012

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Robert G. Wilson v)
• R. G. Batchko, A prime fractal and global quasi-self-similar structure in the distribution of prime-indexed primes, arXiv preprint arXiv:1405.2900 [math.GM], 2014.
• N. Fernandez, An order of primeness.
• N. Fernandez, An order of primeness [cached copy, included with permission of the author]
• Michael P. May, Properties of Higher-Order Prime Number Sequences, Missouri J. Math. Sci. (2020) Vol. 32, No. 2, 158-170; and arXiv version, arXiv:2108.04662 [math.NT], 2021.

Crossrefs

Cf. A000040, A006450, A038580, A049076, A049090, A049202, A057847, A057849, A057850, A057851, A058332, A093047.

Programs

Maple

map(ithprime@@4, select(isprime, [$1..137])); # Peter Luschny, Feb 17 2014

Mathematica

Nest[ Prime, Range[35], 5] (* Robert G. Wilson v, Mar 15 2004 *)

PARI

list(lim)=my(v=List(),q,r,s,t); forprime(p=2,lim, if(isprime(q++) && isprime(r++) && isprime(s++) && isprime(t++), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 16 2017

Formula

a(n) = A000040(A049090(n)). - R. J. Mathar, Jul 07 2012

a(n) ~ n (log n)^5. - Charles R Greathouse IV, Feb 16 2017

Extensions

More terms from Robert G. Wilson v, Nov 10 2000

Name corrected by Sean A. Irvine, Jul 21 2021