cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A132195 Number of three-prime Carmichael numbers less than 10^n.

Original entry on oeis.org

1, 7, 12, 23, 47, 84, 172, 335, 590, 1000, 1858, 3284, 6083, 10816, 19539, 35586, 65309, 120625, 224763, 420658, 790885, 1494738
Offset: 3

Views

Author

Jonathan Vos Post, Nov 19 2007

Keywords

Comments

a(n) = C_3(n) in Table 1, p. 34 of Chick (2007-2008) = card{c such that c is in A002997 INTERSECTION A014612 and c <= 10^n}.

References

  • Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 220.

Links

Crossrefs

For k-prime Carmichael numbers up to 10^n for k = 3,4,...,11, see A132195, A174612, A174613, A174614, A174615, A174616, A174617, A299710, A299711.
Cf. A002997, A006931, A055553.

A299710 Number of ten-prime Carmichael numbers less than 10^n.

Original entry on oeis.org

23, 340, 3058, 20738, 114232, 547528, 2347828
Offset: 16

Views

Author

Tim Johannes Ohrtmann, Feb 17 2018

Keywords

References

  • Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 220.

Links

Crossrefs

For k-prime Carmichael numbers up to 10^n for k = 3,4,...,11, see A132195, A174612, A174613, A174614, A174615, A174616, A174617, A299710, A299711.
Cf. A002997, A006931, A055553.

Extensions

a(22) from Claude Goutier added by Amiram Eldar, Apr 19 2024

A174612 Number of four-prime Carmichael numbers less than 10^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 4, 19, 55, 144, 314, 619, 1179, 2102, 3639, 6042, 9938, 16202, 25758, 40685, 63343, 98253, 151566, 232742
Offset: 0

Views

Author

Michel Lagneau, Mar 23 2010

Keywords

Examples

			For n=5, the smallest Carmichael number with 4 prime factors is 41041 = 7*11*13*41.

References

  • Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 220.

Links

Crossrefs

For k-prime Carmichael numbers up to 10^n for k = 3,4,...,11, see A132195, A174612, A174613, A174614, A174615, A174616, A174617, A299710, A299711.
Cf. A002997, A006931, A055553.

Extensions

a(0) inserted and a(22) from Claude Goutier added by Amiram Eldar, Apr 19 2024

A174614 Number of six-prime Carmichael numbers less than 10^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 99, 459, 1714, 5270, 14401, 36907, 86696, 194306, 414660, 849564, 1681744, 3230120, 6034046
Offset: 0

Views

Author

Michel Lagneau, Mar 23 2010

Keywords

Examples

			For n=9: the smallest Carmichael number with 6 prime factors is 321197185 = 5*19*23*29*37*137.

References

  • Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 220.

Links

Crossrefs

For k-prime Carmichael numbers up to 10^n for k = 3,4,...,11, see A132195, A174612, A174613, A174614, A174615, A174616, A174617, A299710, A299711.
Cf. A002997, A006931, A055553.

Extensions

a(22) from Claude Goutier added by Amiram Eldar, Apr 19 2024

A174615 Number of seven-prime Carmichael numbers less than 10^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 41, 262, 1340, 5359, 19210, 60150, 172234, 460553, 1159167, 2774702, 6363475, 14056367
Offset: 0

Views

Author

Michel Lagneau, Mar 23 2010

Keywords

Examples

			The smallest Carmichael number with 7 prime factors is 5394826801 = 7*13*17*23*31*67*73, and there is one other 10-digit example, so a(10)=2.

References

  • Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 220.

Links

Crossrefs

For k-prime Carmichael numbers up to 10^n for k = 3,4,...,11, see A132195, A174612, A174613, A174614, A174615, A174616, A174617, A299710, A299711.
Cf. A002997, A006931, A055553.

Extensions

a(22) from Claude Goutier added by Amiram Eldar, Apr 19 2024

A174616 Number of eight-prime Carmichael numbers less than 10^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 89, 655, 3622, 16348, 63635, 223997, 720406, 2148017, 6015901, 16005646
Offset: 0

Views

Author

Michel Lagneau, Mar 23 2010

Keywords

Examples

			The smallest Carmichael number with 8 prime factors is 232250619601 = 7*11*13*17*31*37*73*163, and there are 6 others, so a(12) = 7.

References

  • Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 220.

Links

Crossrefs

For k-prime Carmichael numbers up to 10^n for k = 3,4,...,11, see A132195, A174612, A174613, A174614, A174615, A174616, A174617, A299710, A299711.
Cf. A002997, A006931, A055553.

Extensions

a(22) from Claude Goutier added by Amiram Eldar, Apr 19 2024

A174617 Number of nine-prime Carmichael numbers less than 10^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 27, 170, 1436, 8835, 44993, 196391, 762963, 2714473, 8939435
Offset: 0

Views

Author

Michel Lagneau, Mar 23 2010

Keywords

Examples

			The smallest Carmichael number with 9 prime factors is 9746347772161 = 7*11*13*17*19*31*37*41*641, so a(13)=1..

References

  • Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 220.

Links

Crossrefs

For k-prime Carmichael numbers up to 10^n for k = 3,4,...,11, see A132195, A174612, A174613, A174614, A174615, A174616, A174617, A299710, A299711.
Cf. A002997, A006931, A055553.

Extensions

a(22) from Claude Goutier added by Amiram Eldar, Apr 19 2024

A299711 Number of eleven-prime Carmichael numbers less than 10^n.

Original entry on oeis.org

1, 49, 576, 5804, 42764, 262818
Offset: 17

Views

Author

Tim Johannes Ohrtmann, Feb 17 2018

Keywords

Examples

			60977817398996785 = 5*7*17*19*23*37*53*73*79*89*233 is the only Carmichael number with eleven prime factors below 10^17, so a(17) = 1.

Links

Crossrefs

For k-prime Carmichael numbers up to 10^n for k = 3,4,...,11, see A132195, A174612, A174613, A174614, A174615, A174616, A174617, A299710, A299711.
Cf. A002997, A006931, A055553.

Extensions

a(22) from Claude Goutier added by Amiram Eldar, Apr 19 2024

A257035 Numbers m such that 6m+1, 12m+1, 18m+1, 36m+1 and 72m+1 are all prime.

Original entry on oeis.org

1, 121, 380, 506, 511, 3796, 5875, 6006, 8976, 9025, 9186, 10920, 12245, 12896, 14476, 14800, 15386, 22451, 23471, 32326, 35175, 38460, 39536, 40420, 41456, 43430, 44415, 59901, 60076, 61341, 74676, 76615, 76986, 82530, 87390, 99486, 101101, 107926, 112315, 112840, 115101
Offset: 1

Views

Author

M. F. Hasler, Apr 14 2015

Keywords

Comments

A subsequence of A206024, which contains A206349 as a subsequence, see there for motivations.

Links

Crossrefs

Cf. A002997, A112428, A174613, A206024, A206349.

Programs

  • GAP
    Filtered([1..120000],m->IsPrime(6*m+1) and IsPrime(12*m+1) and IsPrime(18*m+1) and IsPrime(36*m+1) and IsPrime(72*m+1)); # Muniru A Asiru, Jun 06 2018
  • Magma
    [n: n in [0..2*10^5] | IsPrime(6*n+1) and IsPrime(12*n+1) and IsPrime(18*n+1) and IsPrime(36*n+1)and IsPrime(72*n+1)]; // Vincenzo Librandi, Apr 15 2015
  • Maple
    f:=isprime: select(m->f(6*m+1) and f(12*m+1) and f(18*m+1) and f(36*m+1) and f(72*m+1),[$1..120000] ); # Muniru A Asiru, Jun 06 2018
  • Mathematica
    Select[Range[120000], PrimeQ[6 # + 1] && PrimeQ[12 # + 1] && PrimeQ[18 # + 1] && PrimeQ[36 # + 1] && PrimeQ[72 # + 1] &] (* Vincenzo Librandi, Apr 15 2015 *)
Select[Range[120000],AllTrue[{6,12,18,36,72}#+1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 23 2016 *)
  • PARI
    is(m,c=72)=!until(bittest(c\=2,0)&&9>c+=3,isprime(m*c+1)||return)
Showing 1-9 of 9 results.

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