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 1-6 of 6 results.

A167135 Primes congruent to {2, 3, 5, 7, 11} mod 12.

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 41, 43, 47, 53, 59, 67, 71, 79, 83, 89, 101, 103, 107, 113, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 191, 197, 199, 211, 223, 227, 233, 239, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 317, 331, 347, 353, 359
Offset: 1

Views

Author

Klaus Brockhaus, Oct 28 2009

Keywords

Comments

Primes p such that p mod 12 is prime.
Primes of the form 12*n+r where n >= 0 and r is in {2, 3, 5, 7, 11}.
Except for the prime 2, these are the primes that are encountered in the set of numbers {x, f(f(x))} where x is of the form 4k+3 with k>=0, and where f(x) is the 3x+1-problem function, and f(f(x)) the second iteration value. Indeed this sequence is the set union of 2 and A002145 (4k+3 primes) and A007528 (6k+5 primes), since f(f(4k+3))=6k+5. Equivalently one does not get any prime from A068228 (the complement of the present sequence). - Michel Marcus and Bill McEachen, May 07 2016

Links

Crossrefs

Subsequences: A002145, A007528. Complement: A068228.
Cf. A003627, A045326, A003631, A045309, A045314, A042987, A078403, A042993, A167134, A167135, A167119: primes p such that p mod k is prime, for k = 3..13 resp.

Programs

  • Magma
    [ p: p in PrimesUpTo(760) | p mod 12 in {2, 3, 5, 7, 11} ];
  • Magma
    [ p: p in PrimesUpTo(760) | exists(t){ n: n in [0..p div 12] | exists(u){ r: r in {2, 3, 5,7, 11} | p eq (12*n+r) } } ];
  • Maple
    isA167135  := n -> isprime(n) and not modp(n, 12) != 1:
select(isA167135, [$1..360]); # Peter Luschny, Mar 28 2018
  • Mathematica
    Select[Prime[Range[400]],MemberQ[{2,3, 5, 7, 11},Mod[#,12]]&] (* Vincenzo Librandi, Aug 05 2012 *)
Select[Prime[Range[72]], Mod[#, 12] != 1 &] (* Peter Luschny, Mar 28 2018 *)

A167119 Primes congruent to 2, 3, 5, 7 or 11 (mod 13).

Original entry on oeis.org

2, 3, 5, 7, 11, 29, 31, 37, 41, 59, 67, 83, 89, 107, 109, 137, 163, 167, 193, 197, 211, 223, 239, 241, 263, 271, 293, 317, 349, 353, 367, 379, 397, 401, 419, 421, 431, 449, 457, 479, 499, 509, 523, 557, 577, 587, 601, 613, 631, 653, 661, 683, 691, 709, 733, 739, 743, 757
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Oct 27 2009

Keywords

Comments

Primes which have a remainder mod 13 that is prime.
Union of A141858, A100202, A102732, A140371 and A140373. - R. J. Mathar, Oct 29 2009

Examples

			11 mod 13 = 11, 29 mod 13 = 3, 31 mod 13 = 5, hence 11, 29 and 31 are in the sequence.

Links

Crossrefs

Cf. A003627, A045326, A003631, A045309, A045314, A042987, A078403, A042993, A167134, A167135: primes p such that p mod k is prime, for k = 3..12 resp.

Programs

  • Magma
    [ p: p in PrimesUpTo(740) | p mod 13 in {2, 3, 5, 7, 11} ]; // Klaus Brockhaus, Oct 28 2009
  • Mathematica
    f[n_]:=PrimeQ[Mod[n,13]]; lst={};Do[p=Prime[n];If[f[p],AppendTo[lst,p]],{n,6,6!}];lst
Select[Prime[Range[4000]],MemberQ[{2, 3, 5, 7, 11},Mod[#,13]]&] (* Vincenzo Librandi, Aug 05 2012 *)
  • PARI
    {forprime(p=2, 740, if(isprime(p%13), print1(p, ",")))} \\ Klaus Brockhaus, Oct 28 2009

Extensions

Edited by Klaus Brockhaus and R. J. Mathar, Oct 28 2009 and Oct 29 2009

A215155 Primes congruent to {2, 3, 5, 7} mod 13.

Original entry on oeis.org

2, 3, 5, 7, 29, 31, 41, 59, 67, 83, 107, 109, 137, 163, 197, 211, 223, 239, 241, 263, 293, 317, 353, 367, 379, 397, 419, 421, 431, 449, 457, 499, 509, 523, 577, 587, 601, 613, 631, 653, 683, 691, 709, 733, 743, 757, 761, 769, 787, 809, 811, 821, 839, 863
Offset: 1

Views

Author

Vincenzo Librandi, Aug 05 2012

Keywords

Links

Crossrefs

Cf. A000040. A167134.

Programs

  • Magma
    [p: p in PrimesUpTo(1000) | p mod 13 in {2, 3, 5, 7} ];
  • Mathematica
    Select[Prime[Range[600]],MemberQ[{2,3, 5, 7},Mod[#,13]]&]

A215156 Primes congruent to {2, 3, 5, 7} mod 17.

Original entry on oeis.org

2, 3, 5, 7, 19, 37, 41, 53, 71, 73, 107, 109, 139, 173, 211, 223, 241, 257, 277, 311, 313, 347, 359, 379, 449, 461, 479, 547, 563, 617, 619, 631, 653, 683, 719, 733, 751, 787, 821, 823, 853, 857, 887, 937, 971, 991, 1039, 1061, 1091, 1093, 1129, 1163, 1193
Offset: 1

Views

Author

Vincenzo Librandi, Aug 05 2012

Keywords

Links

Crossrefs

Cf. A000040, A167134.

Programs

  • Magma
    [ p: p in PrimesUpTo(2000) | p mod 17 in {2, 3, 5, 7} ];
  • Mathematica
    Select[Prime[Range[600]],MemberQ[{2,3, 5, 7},Mod[#,17]]&]

A215157 Primes congruent to {2, 3, 5, 7} mod 19.

Original entry on oeis.org

2, 3, 5, 7, 41, 43, 59, 79, 83, 97, 157, 173, 193, 197, 211, 233, 269, 271, 307, 311, 347, 349, 383, 401, 421, 439, 461, 463, 499, 577, 613, 653, 691, 727, 743, 839, 857, 877, 881, 919, 953, 971, 991, 1009, 1031, 1033, 1069, 1109, 1123, 1181, 1223, 1237
Offset: 1

Views

Author

Vincenzo Librandi, Aug 05 2012

Keywords

Links

Crossrefs

Cf. A000040, A167134.

Programs

  • Magma
    [ p: p in PrimesUpTo(2000) | p mod 19 in {2, 3, 5, 7} ];
  • Mathematica
    Select[Prime[Range[600]],MemberQ[{2,3, 5, 7},Mod[#,19]]&]

A354177 Numbers m such that the four consecutive primes starting at m are congruent to {2, 3, 5, 7} (mod 11).

Original entry on oeis.org

2, 82799, 406661, 447779, 490019, 596279, 617971, 654931, 790781, 1286969, 1532291, 1543357, 1775831, 1916939, 1932911, 2220539, 2240977, 2298749, 2307989, 2376629, 2435039, 2458139, 2513579, 2731049, 2775599, 3093851, 3141899, 3213839, 3294337, 3331319, 3351251, 3366497, 3645193, 3689149, 3733259, 3781153, 3981331
Offset: 1

Views

Author

Zak Seidov, Sep 09 2022

Keywords

Comments

All first differences except for 82799 - 2 = 82797 are multiples of 22.

Examples

			The four consecutive primes {82799, 82811, 82813, 82837} are congruent to {2, 3, 5, 7} (mod 11).

Crossrefs

Subsequence of A167134.

Programs

  • Maple
    R:= 2: count:= 1:
for p from 13 by 22 while count < 37 do
  if not isprime(p) then next fi;
  q:= nextprime(p); if q mod 11 <> 3 then next fi;
  q:= nextprime(q); if q mod 11 <> 5 then next fi;
  q:= nextprime(q); if q mod 11 = 7 then
     count:= count+1; R:= R,p fi
od:
R; # Robert Israel, Sep 14 2022
  • Mathematica
    s = {2}; p1=7; Do[p1 = NextPrime[p1]; p2 = NextPrime[p1]; p3 = NextPrime[p2]; p4 = NextPrime[p3]; If[{2, 3, 5, 7} == Mod[{p1, p2, p3, p4}, 11], AppendTo[s, p1]], {10^6}]; s
Showing 1-6 of 6 results.

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