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 1-3 of 3 results.

A253976 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, (p^6 + 5)/6 and (p^8 + 5)/6 are prime.

Original entry on oeis.org

67103, 7524593, 9938069, 10125793, 13042637, 55741139, 55792241, 58429099, 77618323, 92713879, 94554613, 96242761, 103774049, 119753549, 141725501, 142915193, 164899799, 165227399, 173202247, 174728233, 178411771, 184279409, 184356703, 186622003, 195863347, 200406977, 239488649
Offset: 1

Views

Author

Zak Seidov, Jan 21 2015

Keywords

Links

Crossrefs

Subsequence of A253939. Cf. A118915, A247478, A253939, A253940, A253941.

Programs

  • Mathematica
    Select[Prime[Range[132*10^5]],AllTrue[(#^Range[2,8,2]+5)/6,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 11 2018 *)
  • PARI
    forprime(p=1,10^7,k=0;for(i=1,4,P=(p^(2*i)+5)/6;if(P\1==P,if(ispseudoprime(P),k++);if(!ispseudoprime(P),k=0;break));if(P\1!=P,k=0;break));if(k,print1(p,", "))) \\ Derek Orr, Jan 21 2015

A254039 Primes p such that (p^3 + 2)/3, (p^5 + 2)/3 and (p^7 + 2)/3 are prime.

Original entry on oeis.org

524521, 1090891, 1383391, 2633509, 3371059, 4872331, 7304131, 7756669, 8819119, 8877331, 11536471, 12290851, 13362211, 13509649, 14658499, 15359401, 17094151, 17582329, 18191179, 18550891, 19416259, 20465209, 21971629, 22519531, 22619431, 25972561, 27155881, 29281699
Offset: 1

Views

Author

K. D. Bajpai, Jan 23 2015

Keywords

Comments

All the terms in this sequence are 1 mod 9.

Examples

			a(1) = 524521;
(524521^3 + 2)/3 = 48102471044890921;
(524521^5 + 2)/3 = 13234061480615091039311002201;
(524521^7 + 2)/3 = 3640985160809159281478976663465873196681;
all four are prime.

Links

Crossrefs

Cf. A241120, A253941, A253976, A253940.

Programs

  • Magma
    [p: p in PrimesInInterval(3, 10000000) | IsPrime((p^3 + 2) div 3) and IsPrime((p^5 + 2) div 3) and IsPrime((p^7 + 2) div 3)]; // Vincenzo Librandi, Mar 27 2015
  • Mathematica
    Select[Prime[Range[10^7]], PrimeQ[(#^3 + 2)/3] && PrimeQ[(#^5 + 2)/3] && PrimeQ[(#^7 + 2)/3] &]
  • PARI
    is(n)=n%9==1 && isprime(n) && isprime((n^3+2)/3) && isprime((n^5+2)/3) && isprime((n^7+2)/3) \\ Charles R Greathouse IV, Jan 23 2015

A256811 Primes p such that (p^2+2)/3 and (p^4+2)/3 are prime.

Original entry on oeis.org

37, 521, 881, 1619, 2053, 2213, 2341, 3527, 3637, 3727, 4157, 5147, 7019, 10009, 10891, 12277, 14741, 15913, 16273, 17747, 18757, 24499, 25307, 25577, 26209, 27073, 31481, 31517, 32833, 35083, 36739, 36791, 39079, 40231, 40949, 41039, 42013, 42461, 42767, 47917
Offset: 1

Views

Author

K. D. Bajpai, Apr 15 2015

Keywords

Examples

			a(1) = 37; (37^2 + 2)/3 = 457; (37^4 + 2)/3 = 624721; all three are prime.

Links

Crossrefs

Cf. A241120, A253941, A253976, A253940.

Programs

  • Magma
    [p: p in PrimesUpTo(5*10^4) | IsPrime((p^2+2) div 3)  and IsPrime((p^4+2) div 3 )]; // Vincenzo Librandi, Apr 20 2015
  • Mathematica
    Select[Prime[Range[10^4]], PrimeQ[(#^2 + 2)/3] && PrimeQ[(#^4 + 2)/3] &]
  • PARI
    forprime(p=1,10^5,if(!((p^2+2)%3)&&!((p^4+2)%3)&&isprime((p^2+2)/3)&&isprime((p^4+2)/3),print1(p,", "))) \\ Derek Orr, Apr 16 2015
Showing 1-3 of 3 results.

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

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