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A007821
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Primes p such that pi(p) is not prime.
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72
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2, 7, 13, 19, 23, 29, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373
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OFFSET
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1,1
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COMMENTS
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Primes prime(k) such that A049076(k)=1, sorted along increasing k. - R. J. Mathar, Jan 28 2014
The complement of A006450 (primes with prime index) within the primes A000040.
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REFERENCES
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C. Kimberling, Fractal sequences and interspersions, Ars Combinatoria, vol. 45 p 157 1997.
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..1000
Lubomir Alexandrov, On the nonasymptotic prime number distribution, arXiv:math/9811096 [math.NT], 1998.
N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]
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FORMULA
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A137588(a(n)) = n; a(n) = A000040(A018252(n)). - Reinhard Zumkeller, Jan 28 2008
A000040 = A007821 U A006450. - Juri-Stepan Gerasimov, Sep 24 2009
A175247 U { a(n); n > 1 } = A000040. { a(n) } = { 2 } U { primes (A000040) with composite index (A002808) }. - Jaroslav Krizek, Mar 13 2010
G.f. over nonprime powers: Sum_{k >= 1} prime(k)*x^k-prime(prime(k))*x^prime(k). - Benedict W. J. Irwin, Jun 11 2016
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MAPLE
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A007821 := proc(n) ithprime(A018252(n)) ; end proc: # R. J. Mathar, Jul 07 2012
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MATHEMATICA
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Prime[ Select[ Range[75], !PrimeQ[ # ] &]] (* Robert G. Wilson v, Mar 15 2004 *)
With[{nn=100}, Pick[Prime[Range[nn]], Table[If[PrimeQ[n], 0, 1], {n, nn}], 1]] (* Harvey P. Dale, Aug 14 2020 *)
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PROG
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(Haskell)
a007821 = a000040 . a018252
a007821_list = map a000040 a018252_list
-- Reinhard Zumkeller, Jan 12 2013
(PARI) forprime(p=2, 1e3, if(!isprime(primepi(p)), print1(p, ", "))) \\ Felix Fröhlich, Aug 16 2014
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CROSSREFS
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Cf. A049076, A049078, A049079, A049080, A049081, A058322, A058324, A058325, A058326, A058327, A058328, A093046, A006450.
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.
Sequence in context: A168465 A140562 A155547 * A156007 A067774 A063637
Adjacent sequences: A007818 A007819 A007820 * A007822 A007823 A007824
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KEYWORD
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nonn
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AUTHOR
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Monte J. Zerger (mzerger(AT)cc4.adams.edu), Clark Kimberling
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EXTENSIONS
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Edited by M. F. Hasler, Jul 31 2015
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STATUS
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approved
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