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 1-4 of 4 results.

A248368 Primes p such that 52*p + 1 is prime.

Original entry on oeis.org

3, 13, 31, 43, 73, 109, 139, 151, 181, 193, 211, 223, 229, 283, 349, 379, 409, 421, 463, 523, 601, 619, 691, 769, 823, 853, 1021, 1033, 1069, 1153, 1231, 1279, 1303, 1453, 1459, 1471, 1531, 1663, 1693, 1723, 1741, 1783, 1831, 1873, 1933, 2029, 2131, 2251, 2269, 2293, 2593, 2671, 2749, 2791
Offset: 1

Views

Author

Zak Seidov, Oct 05 2014

Keywords

Comments

Or, primes in A248221. Subsequence of A248221. Note that a(1..6) coincide with A171517(1..6).

Links

Crossrefs

Cf. A033210, A142508, A171517, A248221.

Programs

  • Maple
    A248368:=n->`if`(isprime(52*n+1) and isprime(n), n, NULL): seq(A248368(n), n=1..4000); # Wesley Ivan Hurt, Oct 05 2014
  • Mathematica
    s = {}; Do[If[PrimeQ[1 + 52*(p = Prime[n])], AppendTo[s, p]], {n, 500}]; s
Select[Prime[Range[500]],PrimeQ[52#+1]&] (* Harvey P. Dale, Aug 15 2017 *)
  • PARI
    forprime(p=1,10^4,if(isprime(52*p+1),print1(p,", "))) \\ Derek Orr, Oct 05 2014

A290839 a(n) = smallest prime p such that 2p + 2n - 1 is prime.

Original entry on oeis.org

2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 5, 3, 2, 2, 7, 3, 2, 3, 2, 2, 3, 2, 7, 3, 2, 5, 3, 2, 2, 7, 3, 2, 3, 2, 2, 13, 3, 2, 3, 2, 11, 3, 2, 5, 7, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 13, 7, 11, 5, 19, 3, 2, 3, 2, 5, 3, 2, 2, 7, 5, 5, 3, 2, 2, 7, 3, 2, 13, 3, 2, 3, 2, 7, 3, 2
Offset: 0

Views

Author

XU Pingya, Aug 12 2017

Keywords

Links

Crossrefs

Cf. A005384, A023204, A023205, A023206, A023207, A171517, A020483, A290838.
Cf. A067076 (indices n at which a(n) = 2).

Programs

  • Mathematica
    Table[j=0; found=False; While[!found, j++; found=PrimeQ[2Prime[j]+2n-1]]; Prime[j], {n, 85}]
  • PARI
    a(n) = {my(p=2); while(!isprime(2*p+2*n-1), p = nextprime(p+1)); p;} \\ Michel Marcus, Aug 12 2017

Formula

a(-n) = A290838(n+1). - Iain Fox, Dec 14 2017

Extensions

a(0) prepended by Iain Fox, Dec 14 2017

A171518 Primes p such that 3*p-+8 are primes.

Original entry on oeis.org

5, 7, 13, 17, 53, 73, 83, 113, 127, 157, 193, 223, 277, 347, 367, 433, 613, 647, 673, 743, 797, 907, 937, 1117, 1217, 1373, 1427, 1483, 1543, 1597, 1637, 1667, 1877, 1933, 2027, 2237, 2297, 2447, 2647, 2687, 2843, 3083, 3137, 3613, 3797, 4073, 4463, 4483
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 10 2009

Keywords

Examples

			5 is in the sequence since 3*5-8=7 and 3*5+8=23 are primes.

Links

Crossrefs

Cf. A000040, A005382, A005384, A023204-A023207, A063908-A063912, A103803, A124098, A125272, A171517

Programs

  • Mathematica
    Select[Prime[Range[7! ]],PrimeQ[3*#-8]&&PrimeQ[3*#+8]&]
Select[Prime[Range[700]],AllTrue[3#+{8,-8},PrimeQ]&] (* Harvey P. Dale, Feb 10 2025 *)

A248372 Numbers m such that both p = 52*m + 1 and q = 52*p + 1 are prime.

Original entry on oeis.org

36, 39, 60, 126, 171, 189, 195, 300, 315, 405, 420, 435, 504, 540, 570, 606, 720, 756, 816, 876, 960, 1089, 1221, 1224, 1260, 1329, 1365, 1371, 1389, 1404, 1530, 1554, 1674, 1740, 1785, 1791, 1914, 1959, 2085, 2244, 2304, 2334, 2376, 2451, 2454, 2520, 2631, 2646, 2715, 2799, 2976
Offset: 1

Views

Author

Zak Seidov, Oct 05 2014

Keywords

Comments

All terms are divisible by 3, because if m == 1 or 2 (mod 3), either q or p is divisible by 3.

Links

Crossrefs

Subsequence of A248221.
Cf. A033210, A142508, A171517, A248221, A248368.

Programs

  • Mathematica
    s={};Do[If[PrimeQ[p=52*n+1]&&PrimeQ[52*p+1],AppendTo[s,n]],{n,3000}];s
Select[Range[3000],AllTrue[{52#+1,53+2704#},PrimeQ]&] (* Harvey P. Dale, Mar 21 2025 *)
  • PARI
    for(n=1,10^4,p=52*n+1;if(isprime(p)&&isprime(52*p+1),print1(n,", "))) \\ Derek Orr, Oct 06 2014
Showing 1-4 of 4 results.

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