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 1-7 of 7 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

A067257 Numbers n such that n, 2n+1, 3n+2, 4n+3 are primes.

Original entry on oeis.org

5, 89, 1409, 1889, 10589, 11549, 11909, 12899, 17159, 19889, 22349, 24239, 26189, 35999, 37049, 37379, 39419, 44879, 45569, 49919, 60779, 67559, 68669, 75329, 83579, 88919, 104369, 108359, 112349, 114599, 127139, 133979, 135029, 135449
Offset: 1

Views

Author

Benoit Cloitre, Feb 20 2002

Keywords

Comments

Terms are congruent to {5,29} mod 30. - Zak Seidov, May 31 2012

Links

Crossrefs

Cf. A000040, A005384, A067256, A067258, A101767-A101770.

Programs

  • Magma
    [n: n in [1..150000] | IsPrime(n) and IsPrime(2*n+1) and IsPrime(3*n+2) and IsPrime(4*n+3)]; // Vincenzo Librandi, Oct 31 2014
  • Mathematica
    Select[Prime[Range[10^5]],PrimeQ[2*#+1]&&PrimeQ[3*#+2]&&PrimeQ[4*#+3] &] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2008 *)

Extensions

Extended by Ray Chandler, Dec 31 2004

A067258 Numbers n such that n, 2n+1, 3n+2, 4n+3, 5n+4 are primes.

Original entry on oeis.org

5, 89, 12899, 35999, 45569, 83579, 108359, 154769, 175349, 196769, 206009, 209039, 303029, 374009, 420419, 489179, 513239, 641549, 658349, 709589, 765749, 775949, 862769, 991079, 1018709, 1057019, 1265549, 1527629, 1609739, 1621079
Offset: 1

Views

Author

Benoit Cloitre, Feb 20 2002

Keywords

Comments

Except for 5, all terms == 29 (mod 30). - Robert Israel, May 28 2018

Links

Crossrefs

Cf. A000040, A005384, A067256, A067257, A101767-A101770.

Programs

  • Maple
    select(t -> andmap(isprime, [t,2*t+1,3*t+2,4*t+3,5*t+4]),
[5, seq(i,i=29..2*10^6,30)]); # Robert Israel, May 28 2018
  • Mathematica
    a={};Do[p=Prime[n];If[PrimeQ[p*2+1]&&PrimeQ[p*3+2]&&PrimeQ[p*4+3]&&PrimeQ[p*5+4],AppendTo[a,p]],{n,1,10^5}];Print[a]; (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

Extensions

More terms from Sascha Kurz, Mar 23 2002

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

A101768 Numbers k such that k, 2*k+1, 3*k+2, 4*k+3, 5*k+4, 6*k+5, 7*k+6 are primes.

Original entry on oeis.org

2894219, 5246009, 8189999, 8678669, 13951559, 18160379, 24765509, 38911949, 40645919, 60041519, 64523969, 108405989, 124028309, 126392699, 132767039, 142738679, 189142589, 242024369, 248451839, 325561319, 354218759, 392136359
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 31 2004

Keywords

Crossrefs

Cf. A000040, A005384, A067256-A067258, A101767-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] && PrimeQ[p*7+6], AppendTo[a, p]], {n, 1, 17^5}]; a (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)
Select[Range[4*10^8], And@@PrimeQ[#*Range[7]+Range[0,6]]&] (* Harvey P. Dale, Jul 22 2011 *)

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 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.