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A038580 Primes with indices that are primes with prime indices. 40


%S 5,11,31,59,127,179,277,331,431,599,709,919,1063,1153,1297,1523,1787,

%T 1847,2221,2381,2477,2749,3001,3259,3637,3943,4091,4273,4397,4549,

%U 5381,5623,5869,6113,6661,6823,7193,7607,7841,8221,8527,8719,9319,9461,9739

%N Primes with indices that are primes with prime indices.

%H T. D. Noe, <a href="/A038580/b038580.txt">Table of n, a(n) for n = 1..1000</a>

%H R. G. Batchko, <a href="http://arxiv.org/abs/1405.2900">A prime fractal and global quasi-self-similar structure in the distribution of prime-indexed primes</a>, arXiv preprint arXiv:1405.2900 [math.GM], 2014.

%H Robert E. Dressler, S. Thomas Parker, <a href="http://dx.doi.org/10.1145/321892.321900">Primes with a prime subscript</a>, J. ACM, Volume 22 Issue 3, July 1975, 380-381.

%H N. Fernandez, <a href="http://www.borve.org/primeness/FOP.html">An order of primeness, F(p)</a>

%H N. Fernandez, <a href="/A006450/a006450.html">An order of primeness</a> [cached copy, included with permission of the author]

%H N. Fernandez, <a href="http://www.borve.org/primeness/moreterms.html">More terms of this and other sequences related to A049076.</a>

%F a(n) = prime(prime(prime(n))).

%F a(n) ~ n*log(n)^3. - _Ilya Gutkovskiy_, Jul 17 2016

%p a:= ithprime@@3;

%p seq(a(n), n=1..50); # _Alois P. Heinz_, Jun 14 2015

%p # For Maple code for the prime/nonprime compound sequences (listed in cross-references) see A003622. - _N. J. A. Sloane_, Mar 30 2016

%t Table[ Prime[ Prime[ Prime[ n ] ] ], {n, 1, 60} ]

%t Nest[Prime, Range[45], 3] (* _Robert G. Wilson v_, Mar 15 2004 *)

%o (PARI) a(n) = prime(prime(prime(n))) \\ _Charles R Greathouse IV_, Apr 28 2015

%o (PARI) list(lim)=my(v=List(),q,r); forprime(p=2,lim, if(isprime(q++) && isprime(r++), listput(v,p))); Set(v) \\ _Charles R Greathouse IV_, Feb 14 2017

%o (MAGMA) [NthPrime(NthPrime(NthPrime(n))): n in [1..50]]; // _Vincenzo Librandi_, Jul 17 2016

%Y Primes p for which A049076(p) > 3.

%Y Cf. A049090, A049202, A049203, A057847, A057849, A057850, A057851, A058332, A093047.

%Y Second differences give A245175.

%Y 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.

%K easy,nice,nonn

%O 1,1

%A _Brian Galebach_

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Last modified November 19 16:37 EST 2019. Contains 329323 sequences. (Running on oeis4.)