A038580 -id:A038580 - cp's OEIS frontend

A102615 Nonprime numbers of order 2.

1, 8, 10, 14, 15, 16, 20, 22, 24, 25, 27, 30, 32, 33, 35, 36, 38, 39, 40, 44, 46, 48, 49, 50, 51, 54, 55, 56, 58, 62, 63, 64, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 82, 85, 86, 87, 88, 90, 92, 93, 94, 96, 99, 100, 102, 104, 105, 108, 110, 111, 114, 115, 116, 117, 118, 120

Offset: 1

Cino Hilliard, Jan 31 2005

nonn

nps(n,0) -> list nonprime(n) or the sequence of nonprime numbers. nps(n,1) -> list nonprime(nonprime(n)) or nps of order 1 nps(n,2) -> list nonprime(nonprime(nonprime(n))) or nps of order 2 ..... The order is the number of nestings - 1. We avoid the nestings in the script with a loop.

Nonprimes (A018252) with nonprime (A018252) subscripts. a(n) U A078782(n) = A018252(n), a(n+1) U A175250(n) = A018252(n) for n >= 1. a(n) = nonprime(nonprime(n)) = A018252(A018252(n)). a(4) = 14 because a(4) = b(b(4)) = b(8) = 14, b = nonprime. a(1) = 1, a(n) = nonprimes (A018252) with composite (A002808) subscripts for n >=2. [Jaroslav Krizek, Mar 13 2010]

			Nonprime(2) = 4.
Nonprime(4) = 8 the second entry.

Cf. A018252.

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, A270796, A102216.

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

nonPrime[n_] := FixedPoint[n + PrimePi[ # ] &, n]; Nest[nonPrime, Range[66], 2] (* Robert G. Wilson v, Feb 04 2005 *)

\We perform nesting(s) with a loop. cics(n,m) = { local(x,y,z); for(x=1,n, z=x; for(y=1,m+1, z=composite(z); ); print1(z",") ) } composite(n) = \ The n-th composite number. 1 is defined as a composite number. { local(c,x); c=1; x=0; while(c <= n, x++; if(!isprime(x),c++); ); return(x) }

Edited by Robert G. Wilson v, Feb 04 2005

A078782 Nonprimes (A018252) with prime (A000040) subscripts.

Original entry on oeis.org

4, 6, 9, 12, 18, 21, 26, 28, 34, 42, 45, 52, 57, 60, 65, 74, 81, 84, 91, 95, 98, 106, 112, 119, 128, 133, 135, 141, 143, 147, 165, 170, 177, 180, 192, 195, 203, 209, 214, 220, 228, 231, 244, 246, 250, 253, 267, 284, 288, 290, 295, 301, 303, 316, 323, 329, 336

Offset: 1

Joseph L. Pe, Jan 09 2003

a(n) = A018252(A000040(n)). Subsequence of A175250 (nonprimes (A018252) with noncomposite (A008578) subscripts), a(n) = A175250(n+1). a(n) U A102615(n) = A018252(n). [From Jaroslav Krizek, Mar 13 2010]

			a(4) = nonprime(prime(4)) = nonprime(7) = 12.

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, A270796, A102216.

from sympy import prime, composite
def A078782(n): return composite(prime(n)-1) # Chai Wah Wu, Nov 13 2024

Corrected by Jaroslav Krizek, Mar 13 2010

A057847 Primes p whose order of primeness A078442(p) is at least 10.

Original entry on oeis.org

648391, 9737333, 174440041, 718064159, 3657500101, 7069067389, 16123689073, 22742734291, 36294260117, 64988430769, 88362852307, 136395369829, 175650481151, 200147986693, 243504973489, 318083817907, 414507281407

Offset: 1

Robert G. Wilson v, Nov 10 2000

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 221 terms from Robert G. Wilson v)
N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A078442, A000040, A006450, A038580, A049090, A049203, A049202, A057849, A057850, A057851, A058332, A093047.

Nest[ Prime, Range[35], 10] (* Robert G. Wilson v, Mar 15 2004 *)

a(n)=my(k=11);while(k--,n=prime(n));n \\ Charles R Greathouse IV, Feb 24 2017

a(n) = prime(A057851(n)). - Andrew Howroyd, Nov 17 2024

Name clarified by Andrew Howroyd, Nov 17 2024

A057849 Primes p whose order of primeness A078442(p) is at least 7.

Original entry on oeis.org

709, 5381, 52711, 167449, 648391, 1128889, 2269733, 3042161, 4535189, 7474967, 9737333, 14161729, 17624813, 19734581, 23391799, 29499439, 37139213, 38790341, 50728129, 56011909, 59053067, 68425619, 77557187, 87019979, 101146501, 113256643, 119535373, 127065427

Offset: 1

Robert G. Wilson v, Nov 10 2000

nonn

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

Cf. A078442, A000040, A006450, A038580, A049090, A049203, A049202, A057850, A057851, A057847, A058332, A093047.

a:= ithprime@@7;
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 14 2015

Nest[ Prime, Range[35], 7] (* Robert G. Wilson v, Mar 15 2004 *)

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

Name clarified by Andrew Howroyd, Nov 17 2024

A057850 Primes p whose order of primeness A078442(p) is at least 8.

Original entry on oeis.org

5381, 52711, 648391, 2269733, 9737333, 17624813, 37139213, 50728129, 77557187, 131807699, 174440041, 259336153, 326851121, 368345293, 440817757, 563167303, 718064159, 751783477, 997525853, 1107276647, 1170710369, 1367161723

Offset: 1

Robert G. Wilson v, Nov 10 2000

nonn

Union of A058325-A058328, A093046 etc. - R. J. Mathar, Jul 07 2012

Robert G. Wilson v, Table of n, a(n) for n = 1..11457
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]

Cf. A078442, A000040, A006450, A038580, A049090, A049203, A049202, A057849, A057851, A057847, A058332, A093047.

Nest[ Prime, Range[35], 8] (* Robert G. Wilson v, Mar 15 2004 *)

list(lim)=my(v=List(), q, r, s, t, u, vv, w); forprime(p=2, lim, if(isprime(q++) && isprime(r++) && isprime(s++) && isprime(t++) && isprime(u++) && isprime(vv++) && isprime(w++), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 19 2017

a(n) = A049090(A049090(n)). - James G. Merickel, Feb 14 2010

a(n) = A000040(A057849(n)). - R. J. Mathar, Jul 07 2012

Name clarified by Andrew Howroyd, Nov 17 2024

A057851 Primes p whose order of primeness A078442(p) is at least 9.

Original entry on oeis.org

52711, 648391, 9737333, 37139213, 174440041, 326851121, 718064159, 997525853, 1559861749, 2724711961, 3657500101, 5545806481, 7069067389, 8012791231, 9672485827, 12501968177, 16123689073, 16917026909, 22742734291

Offset: 1

Robert G. Wilson v, Nov 10 2000

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1381 terms from Robert G. Wilson v)
N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A078442, A000040, A006450, A038580, A049090, A049203, A049202, A057849, A057850, A057847, A058332, A093047.

Nest[ Prime, Range[35], 9] (* Robert G. Wilson v, Mar 15 2004 *)

list(lim)=my(v=List(), q, r, s, t, u, vv, w, x); forprime(p=2, lim, if(isprime(q++) && isprime(r++) && isprime(s++) && isprime(t++) && isprime(u++) && isprime(vv++) && isprime(w++) && isprime(x++), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 19 2017

Name clarified by Andrew Howroyd, Nov 17 2024

A058332 Primes p whose order of primeness A078442(p) is at least 11.

Original entry on oeis.org

9737333, 174440041, 3657500101, 16123689073, 88362852307, 175650481151, 414507281407, 592821132889, 963726515729, 1765037224331, 2428095424619, 3809491708961, 4952019383323, 5669795882633, 6947574946087, 9163611272327

Offset: 1

Robert G. Wilson v, Dec 12 2000

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..47.
N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A078442, A000040, A006450, A038580, A049090, A049203, A049202, A057849, A057850, A057851, A057847, A093047.

Nest[ Prime, Range[35], 11] (* Robert G. Wilson v, Mar 15 2004 *)

a(n) = prime(A057847(n)). - Andrew Howroyd, Nov 17 2024

Name clarified by Andrew Howroyd, Nov 17 2024

A093047 Primes p whose order of primeness A078442(p) is at least 12.

Original entry on oeis.org

174440041, 3657500101, 88362852307, 414507281407, 2428095424619, 4952019383323, 12055296811267, 17461204521323, 28871271685163, 53982894593057, 75063692618249, 119543903707171, 156740126985437, 180252380737439, 222334565193649

Offset: 1

Robert G. Wilson v, Mar 15 2000

Primes p whose primeness is > 12: 3657500101, 88362852307, 2428095424619, 12055296811267, 75063692618249, 156740126985437, ..., . - Robert G. Wilson v, Mar 15 2000

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

Cf. A078442, A000040, A006450, A038580, A049090, A049203, A049202, A057849, A057850, A057851, A057847, A058332, A093047.

Nest[ Prime, Range[35], 12] (* Robert G. Wilson v, Mar 15 2004 *)

a(n) = A058332(prime(n)). - Andrew Howroyd, Nov 17 2024

Name clarified by Andrew Howroyd, Nov 17 2024

A102617 Primes p(n) such that n is a second-order nonprime number.

Original entry on oeis.org

2, 19, 29, 43, 47, 53, 71, 79, 89, 97, 103, 113, 131, 137, 149, 151, 163, 167, 173, 193, 199, 223, 227, 229, 233, 251, 257, 263, 271, 293, 307, 311, 317, 337, 347, 349, 359, 379, 383, 389, 397, 409, 421, 439, 443, 449, 457, 463, 479, 487, 491, 503, 523, 541

Offset: 1

Cino Hilliard, Jan 31 2005

nonn

The prime/nonprime compound sequence ABB. - N. J. A. Sloane, Apr 06 2016

			Nonprime(4) = 8.
The 8th prime is 19, the second entry.

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, A270796, A102216.

For Maple code for the prime/nonprime compound sequences (listed in cross-references) see A003622. - N. J. A. Sloane, Mar 30 2016

nonPrime[n_Integer] := FixedPoint[n + PrimePi[ # ] &, n]; Prime /@ nonPrime /@ nonPrime /@ Range[54] (* Robert G. Wilson v, Feb 04 2005 *)

\We perform nesting(s) with a loop. cips(n,m) = { local(x,y,z); for(x=1,n, z=x; for(y=1,m+1, z=composite(z); ); print1(prime(z)",") ) } composite(n) = \ The n-th composite number. 1 is defined as a composite number. { local(c,x); c=1; x=0; while(c <= n, x++; if(!isprime(x),c++); ); return(x) }

Edited by Robert G. Wilson v, Feb 04 2005

A270792 The prime/nonprime compound sequence ABA.

Original entry on oeis.org

7, 13, 23, 37, 61, 73, 101, 107, 139, 181, 197, 239, 269, 281, 313, 373, 419, 433, 467, 499, 521, 577, 613, 653, 719, 751, 761, 811, 823, 853, 977, 1013, 1051, 1069, 1163, 1187, 1237, 1289, 1307, 1373, 1439, 1453, 1549, 1559, 1583

Offset: 1

N. J. A. Sloane, Mar 30 2016

nonn

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, A270796, A102216.

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

cp's OEIS Frontend

A102615 Nonprime numbers of order 2.

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A078782 Nonprimes (A018252) with prime (A000040) subscripts.

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A057847 Primes p whose order of primeness A078442(p) is at least 10.

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A057849 Primes p whose order of primeness A078442(p) is at least 7.

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A057850 Primes p whose order of primeness A078442(p) is at least 8.

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A057851 Primes p whose order of primeness A078442(p) is at least 9.

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A058332 Primes p whose order of primeness A078442(p) is at least 11.

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A093047 Primes p whose order of primeness A078442(p) is at least 12.

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