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 1-5 of 5 results.

A067256 Numbers n such that n, 2n+1, 3n+2 are primes.

Original entry on oeis.org

3, 5, 23, 29, 83, 89, 173, 233, 239, 293, 419, 659, 953, 1013, 1223, 1409, 1559, 1583, 1889, 2003, 2129, 2339, 2549, 2693, 2939, 3359, 3389, 3593, 3803, 4349, 4373, 4409, 4919, 4943, 5333, 6113, 6173, 8093, 8273, 8513, 9059, 9479, 9539, 10163, 10313
Offset: 1

Views

Author

Benoit Cloitre, Feb 20 2002

Keywords

Comments

a(n)*(2a(n)+1)*(3a(n)+2) are Lucas-Carmichael numbers for n > 1. Analogous to A174734 as A006972 (Lucas-Carmichael numbers) is analogous to A002997 (Carmichael numbers). - Amiram Eldar, Aug 11 2017

Links

Crossrefs

Cf. A000040, A005384, A006972, A067257, A067258, A101767, A101768, A101769, A101770, A174734, A216925.

Programs

A101767 Numbers n such that n, 2n+1, 3n+2, 4n+3, 5n+4, 6n+5 are primes.

Original entry on oeis.org

154769, 175349, 641549, 658349, 1018709, 2274089, 2894219, 5246009, 6621929, 7949759, 8189999, 8678669, 10366439, 12327629, 13951559, 18160379, 18924569, 21914339, 22279949, 22297799, 24765509, 25592279, 31029389, 31835159, 36802079, 38844119, 38911949
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 31 2004

Keywords

Comments

a(n) == 209 (mod 210) - John Cerkan, Mar 22 2018

Links

Crossrefs

Cf. A000040, A005384, A067256, A067257, A067258, A101768, A101769, A101770.

Programs

  • Mathematica
    a={}; Do[p=Prime[n]; If[PrimeQ[p*2+1]&&PrimeQ[p*3+2]&&PrimeQ[p*4+3]&&PrimeQ[p*5+4]&&PrimeQ[p*6+5], AppendTo[a, p]], {n, 1, 10^5}]; Print[a]; (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

Extensions

Terms a(25) and beyond from John Cerkan, Mar 22 2018

A101770 Numbers n such that n, 2n+1, 3n+2, 4n+3, 5n+4, 6n+5, 7n+6, 8n+7, 9n+8 are primes.

Original entry on oeis.org

407874179, 1674689729, 6380217479, 15002412599, 24291715139, 28081637219, 34274541839, 37048322849, 45785202539, 53434060679, 100061694809, 101245430999, 103024911989, 127890675989, 130173995279, 141481942139, 149397940019, 177352532069, 212815427999, 214580145779, 294249502259, 296754699779
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 31 2004

Keywords

Comments

All terms == 2099 or 2309 (mod 2310). - Robert Israel, Jul 05 2016

Links

Crossrefs

Cf. A000040, A005384, A067256, A067257, A067258, A101767, A101768, A101769.

Programs

  • Maple
    select(n -> andmap(isprime,
[n,2*n+1,3*n+2,4*n+3,5*n+4,6*n+5,7*n+6,8*n+7,9*n+8]),
[seq(seq(2310*i+j, j=[2099,2309]),i=0..10^7)]); # Robert Israel, Jul 05 2016

Extensions

More terms from Jens Kruse Andersen, May 08 2008

A101769 Numbers p such that p, 2p+1, 3p+2, 4p+3, 5p+4, 6p+5, 7p+6, 8p+7 are primes.

Original entry on oeis.org

2894219, 60041519, 64523969, 242024369, 407874179, 1092040949, 1092075389, 1674689729, 2281060319, 5035134509, 5329406669, 5683382879, 5792424329, 6000216809, 6380217479, 10409580719, 11488703939, 13745865209, 14181824369, 14904963149, 15002412599, 15412603919
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 31 2004

Keywords

Comments

From Jeppe Stig Nielsen, Jul 07 2020: (Start)
Each term is -1 modulo 210.
The subset p, 2p+1, 4p+3, 8p+7 is a Cunningham chain, cf. A023272. (End)

Links

Crossrefs

Cf. A000040, A005384, A023272, A067256, A067257, A067258, A101767, A101768, A101769, A101770, A336060.

Programs

  • Maple
    R:= NULL: count:= 0:
for i from 0 while count < 50 do
  for j in [1049,2099, 2309] do
    p:= 2310*i+j;
    if andmap(isprime,[p, 2*p + 1, 3*p + 2, 4*p + 3, 5*p + 4, 6*p + 5, 7*p + 6, 8*p + 7]) then
      count:= count+1; R:= R,p;
    fi
od od:
R; # Robert Israel, May 21 2025
  • Mathematica
    a={}; Do[p=Prime[n]; If[PrimeQ[p*2+1]&&PrimeQ[p*3+2]&&PrimeQ[p*4+3]&&PrimeQ[p*5+4]&&PrimeQ[p*6+5]&&PrimeQ[p*7+6]&&PrimeQ[p*8+7], AppendTo[a, p]], {n, 1, 10^7}]; Print[a]; (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

Extensions

a(20)-a(22) from Jeppe Stig Nielsen, Jul 07 2020

A101779 a(n) = least k such that all of k, 2k+1, 3k+2, ..., nk+n-1 are primes, or 0 if no such k is found.

Original entry on oeis.org

2, 2, 3, 5, 5, 154769, 2894219, 2894219, 407874179, 214580145779, 9448481062019, 247236503934419, 2545206711847799, 18178612369988250179, 53792264108455702829
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Jan 13 2005

Keywords

Comments

a(10) > 3691000000, Robert G. Wilson v, Mar 23 2007
By definition the same as A088651(n)-1 if k exists. It is conjectured k always exists. - a(10)-a(15) from Jens Kruse Andersen, May 02 2008

Crossrefs

Cf. A000040, A005384, A067256, A067257, A067258, A101767, A101768, A101769, A101770.
Cf. A088651.

Programs

  • Mathematica
    f[1] = 2; f[n_] := f[n] = Block[{k = PrimePi@ f[n - 1], p, t = Table[i*p + (i - 1), {i, 2, n}]}, While[p = Prime@k; Union@PrimeQ@t != {True}, k++ ]; p]; Do[ Print[f@n // Timing], {n, 10}] (* Robert G. Wilson v, Mar 23 2007 *)

Extensions

a(10)-a(15) from Jens Kruse Andersen, May 02 2008
Showing 1-5 of 5 results.

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