A049078 -id:A049078 - cp's OEIS frontend

A058328 Primes for which A049076(p) = 12.

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.

A102615 Nonprime numbers of order 2.

Original entry on oeis.org

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

A058325 Primes for which A049076(p) = 9.

Original entry on oeis.org

5381, 2269733, 17624813, 50728129, 77557187, 131807699, 259336153, 368345293, 440817757, 563167303, 751783477, 1107276647, 1170710369, 1367161723, 1760768239, 2062666783, 2323114841, 2458721501, 2621760397, 2860139341

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, A058326, A058327, A058328, A093046, A006450.

Nest[ Prime, Select[ Range[30], !PrimeQ[ # ] &], 8] (* Robert G. Wilson v, Mar 15 2004 *)

a(n) = A000040(A058324(n)). - R. J. Mathar, Jul 07 2012

A058326 Primes for which A049076(p) = 10.

Original entry on oeis.org

52711, 37139213, 326851121, 997525853, 1559861749, 2724711961, 5545806481, 8012791231, 9672485827, 12501968177, 16917026909, 25366202179, 26887732891, 31621854169, 41192432219, 48596930311, 55022031709, 58379844161

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, A058327, A058328, A093046, A006450.

Nest[ Prime, Select[ Range[30], !PrimeQ[ # ] &], 9] (* Robert G. Wilson v, Mar 15 2004 *)

a(n) = A000040(A058325(n)). - R. J. Mathar, Jul 07 2012

A058327 Primes for which A049076(p) = 11.

Original entry on oeis.org

648391, 718064159, 7069067389, 22742734291, 36294260117, 64988430769, 136395369829, 200147986693, 243504973489, 318083817907, 435748987787, 664090238153, 705555301183, 835122557939, 1099216100167, 1305164025929

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, A058328, A093046, A006450.

Nest[ Prime, Select[ Range[30], !PrimeQ[ # ] &], 10] (* Robert G. Wilson v, Mar 15 2004 *)

a(n) = A000040(A058326(n)). - R. J. Mathar, Jul 07 2012

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

A270794 The prime/nonprime compound sequence BAA.

Original entry on oeis.org

6, 9, 18, 26, 45, 57, 81, 91, 112, 143, 165, 203, 228, 244, 267, 303, 345, 354, 411, 437, 454, 495, 530, 564, 623, 668, 687, 714, 728, 749, 856, 893, 931, 959, 1032, 1054, 1104, 1158, 1185, 1233, 1268, 1298, 1372, 1392, 1425, 1445, 1539, 1672, 1698, 1714, 1742, 1773, 1802, 1886, 1914, 1966, 2031, 2050, 2104

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

A058328 Primes for which A049076(p) = 12.

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A093046 Primes for which A049076(p) = 13.

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A102615 Nonprime numbers of order 2.

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

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A058325 Primes for which A049076(p) = 9.

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A058326 Primes for which A049076(p) = 10.

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A058327 Primes for which A049076(p) = 11.

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

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