A049076 -id:A049076 - cp's OEIS frontend

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

Neil Fernandez

nonn

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

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]

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.

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

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

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

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

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

A049081 Primes prime(k) for which A049076(k) = 5.

Original entry on oeis.org

31, 1787, 8527, 19577, 27457, 42043, 72727, 96797, 112129, 137077, 173867, 239489, 250751, 285191, 352007, 401519, 443419, 464939, 490643, 527623, 683873, 718807, 755387, 839483, 864013, 985151, 1021271, 1080923, 1159901, 1278779

Offset: 1

Neil Fernandez

Jens Kruse Andersen, Table of n, a(n) for n = 1..1000
N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A049076, A007821, A049078, A049079, A049080, A058322, A058324, A058325, A058326, A058327, A058328, A093046, A006450.

A049081 := proc(n)
        ithprime(A049080(n)) ;
end proc: # R. J. Mathar, Jul 07 2012

Nest[ Prime, Select[ Range[44], !PrimeQ[ # ] &], 5] (* Robert G. Wilson v, Mar 15 2004 *)

More terms from Robert G. Wilson v, Dec 12 2000

A049079 Primes prime(k) for which A049076(k) = 3.

Original entry on oeis.org

5, 59, 179, 331, 431, 599, 919, 1153, 1297, 1523, 1847, 2381, 2477, 2749, 3259, 3637, 3943, 4091, 4273, 4549, 5623, 5869, 6113, 6661, 6823, 7607, 7841, 8221, 8719, 9461, 9739, 9859, 11743, 11953, 12097, 12301, 12547, 13469, 13709, 14177, 14723, 14867

Offset: 1

Neil Fernandez

nonn

N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A049076, A007821, A049078, A049080, A049081, A058322, A058324, A058325, A058326, A058327, A058328, A093046, A006450.

A049079 := proc(n)
        ithprime(A049078(n)) ;
end proc: # R. J. Mathar, Jul 07 2012

Nest[ Prime, Select[ Range[60], !PrimeQ[ # ] &], 3] (* Robert G. Wilson v, Mar 15 2004 *)

Definition edited by Zak Seidov, Sep 15 2013

A049090 Primes for which A049076 >= 4.

Original entry on oeis.org

11, 31, 127, 277, 709, 1063, 1787, 2221, 3001, 4397, 5381, 7193, 8527, 9319, 10631, 12763, 15299, 15823, 19577, 21179, 22093, 24859, 27457, 30133, 33967, 37217, 38833, 40819, 42043, 43651, 52711, 55351, 57943, 60647, 66851, 68639, 72727

Offset: 1

Neil Fernandez

nonn

Union of A049080, A049081, A058322, A058324, etc. - R. J. Mathar, Jul 07 2012

Michael De Vlieger, Table of n, a(n) for n = 1..10000 (first 1000 terms 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, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]
N. Fernandez, More terms of this and other sequences related to A049076.

Cf. A000040, A006450, A038580, A049076, A049202, A049203, A057847, A057849, A057850, A057851, A058332, A093047.

map(ithprime@@3, select(isprime, [$1..157])); # Peter Luschny, Feb 17 2014

Nest[ Prime, Range[40], 4] (* Robert G. Wilson v, Mar 15 2004 *)

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

a(n) = A006450(A006450(n)). - James G. Merickel, Feb 14 2010
a(n) = A000040(A038580(n)). - R. J. Mathar, Jul 07 2012
a(n) ~ n (log n)^4. - Charles R Greathouse IV, Feb 16 2017

Name corrected by Sean A. Irvine, Jul 18 2021

A058322 Primes for which A049076(p) = 7.

Original entry on oeis.org

127, 15299, 87803, 219613, 318211, 506683, 919913, 1254739, 1471343, 1828669, 2364361, 3338989, 3509299, 4030889, 5054303, 5823667, 6478961, 6816631, 7220981, 7807321, 10311439, 10875143, 11469013, 12838937, 13243033, 15239333, 15837299, 16827557, 18143603

Offset: 1

Robert G. Wilson v, Dec 12 2000

nonn

N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A049076, A007821, A049078, A049079, A049080, A049081, A058324, A058325, A058326, A058327, A058328, A093046, A006450.

A058322 := proc(n)
        ithprime(A049081(n)) ;
end proc: # R. J. Mathar, Jul 07 2012
# second Maple program:
map(ithprime@@6, remove(isprime, [$1..42]))[];  # Alois P. Heinz, Mar 15 2020

Nest[ Prime, Select[ Range[40], !PrimeQ[ # ] &], 6] (* Robert G. Wilson v, Mar 15 2004 *)

a(n) = A000040(A049081(n)).

More terms from Alois P. Heinz, Mar 15 2020

A049080 Primes prime(k) for which A049076(k) = 4.

Original entry on oeis.org

11, 277, 1063, 2221, 3001, 4397, 7193, 9319, 10631, 12763, 15823, 21179, 22093, 24859, 30133, 33967, 37217, 38833, 40819, 43651, 55351, 57943, 60647, 66851, 68639, 77431, 80071, 84347, 90023, 98519, 101701, 103069, 125113, 127643

Offset: 1

Neil Fernandez

nonn

Jens Kruse Andersen, 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]

Cf. A049076, A007821, A049078, A049079, A049081, A058322, A058324, A058325, A058326, A058327, A058328, A093046, A006450.

A049080 := proc(n)
        ithprime(A049079(n)) ;
end proc: # R. J. Mathar, Jul 07 2012

Nest[ Prime, Select[ Range[50], !PrimeQ[ # ] &], 4] (* Robert G. Wilson v, Mar 15 2004 *)

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

Original entry on oeis.org

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

Neil Fernandez

nonn

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

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.

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

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

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

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

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

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

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

Name corrected by Sean A. Irvine, Jul 21 2021

A058324 Primes for which A049076(p) = 8.

Original entry on oeis.org

709, 167449, 1128889, 3042161, 4535189, 7474967, 14161729, 19734581, 23391799, 29499439, 38790341, 56011909, 59053067, 68425619, 87019979, 101146501, 113256643, 119535373, 127065427, 138034009, 185350441, 196100297, 207460717, 233784751, 241568891, 280256489

Offset: 1

Robert G. Wilson v, Dec 12 2000

nonn

N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A049076, A007821, A049078, A049079, A049080, A049081, A058322, A058325, A058326, A058327, A058328, A093046, A006450.

map(ithprime@@7, remove(isprime, [$1..38]))[];  # Alois P. Heinz, Mar 15 2020

Nest[ Prime, Select[ Range[34], !PrimeQ[ # ] &], 7] (* Robert G. Wilson v, Mar 15 2004 *)

a(n) = A000040(A058322(n)). - R. J. Mathar, Jul 07 2012

More terms from Alois P. Heinz, Mar 15 2020

A058328 Primes for which A049076(p) = 12.

Original entry on oeis.org

9737333, 16123689073, 175650481151, 592821132889, 963726515729, 1765037224331, 3809491708961, 5669795882633, 6947574946087, 9163611272327, 12695664159413, 19638537755027, 20909033866927, 24894639811901

Offset: 1

Robert G. Wilson v, Dec 12 2000

nonn

N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A049076, A007821, A049078, A049079, A049080, A049081, A058322, A058324, A058325, A058326, A058327, A093046, A006450.

Nest[ Prime, Select[ Range[30], !PrimeQ[ # ] &], 11] (* Robert G. Wilson v, Mar 15 2004 *)

a(n) = A000040(A058327(n)). - R. J. Mathar, Jul 07 2012

A093046 Primes for which A049076(p) = 13.

Original entry on oeis.org

174440041, 414507281407, 4952019383323, 17461204521323, 28871271685163, 53982894593057, 119543903707171, 180252380737439, 222334565193649, 295872998567819, 414190707114539, 649544694886663, 692919372869953, 829484152743469, 1111923751842437, 1335294947809661, 1532021237514419, 1635795965187779

Offset: 1

Robert G. Wilson v, Mar 15 2000

nonn

N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A049076, A007821, A049078, A049079, A049080, A049081, A058322, A058324, A058325, A058326, A058327, A058328, A006450.

Nest[ Prime, Select[ Range[30], !PrimeQ[ # ] &], 12]

a(n) = A000040(A058328(n)). - R. J. Mathar, Jul 07 2012

a(7)-a(9) from Robert G. Wilson v, Dec 27 2005

a(10)-a(18) from Robert G. Wilson v, Mar 08 2017 using Kim Walisch's primecount.

cp's OEIS Frontend

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

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A049081 Primes prime(k) for which A049076(k) = 5.

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A049079 Primes prime(k) for which A049076(k) = 3.

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A049090 Primes for which A049076 >= 4.

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A058322 Primes for which A049076(p) = 7.

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A049080 Primes prime(k) for which A049076(k) = 4.

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

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