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.

A253940 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, and (p^8 + 5)/6 are prime.

Original entry on oeis.org

39367, 52163, 67103, 79631, 100981, 280547, 318457, 530711, 605123, 815401, 833923, 834947, 928871, 1313857, 1734067, 1750069, 1800973, 2163979, 2427137, 2598119, 2611027, 2754991, 2764187, 2836259, 3040757, 3101309, 3118697, 3465953, 3646693, 4014809
Offset: 1

Views

Author

Zak Seidov, Jan 20 2015

Keywords

Links

Crossrefs

Subsequence of A253925. Cf. A118915, A247478, A253939.

Programs

  • Magma
    [p: p in PrimesUpTo(10^7) | IsPrime((p^2+5) div 6) and IsPrime((p^4+5) div 6) and IsPrime((p^8+5) div 6)]; // Vincenzo Librandi, Jan 21 2015
  • Mathematica
    Select[Prime[Range[10^6]], PrimeQ[(#^2 + 5) / 6] &&PrimeQ[(#^4 + 5) / 6] &&PrimeQ[(#^8 + 5) / 6] &] (* Vincenzo Librandi, Jan 21 2015 *)
Select[Prime[Range[300000]],AllTrue[({#^2,#^4,#^8}+5)/6,PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 15 2021 *)

A253925 Primes p such that both (p^2 + 5)/6 and (p^4 + 5)/6 are prime.

Original entry on oeis.org

127, 1009, 1709, 2087, 2393, 2969, 3221, 3347, 7309, 7757, 7883, 10529, 11411, 12923, 17569, 18269, 21799, 23311, 23633, 24877, 25703, 26839, 27091, 29429, 35461, 35603, 38431, 39367, 39761, 41887, 42967, 43037, 45361, 45989, 47699, 52163, 59093, 63629, 65323, 67103, 68041, 69481, 70937, 74843, 77813, 77867
Offset: 1

Views

Author

Zak Seidov, Jan 19 2015

Keywords

Comments

Intersection of A118915 and A247478.

Examples

			a(1)=127=A118915(9)=A247478(9). a(2)=1009=A118915(45)=A247478(22).

Links

Crossrefs

Cf. A118915, A247478.

Programs

  • PARI
    forprime(p=5,1e6,if(isprime((p^2+5)/6) && isprime((p^4+5)/6), print1(p", "))) \\ Charles R Greathouse IV, Jan 19 2015

A253941 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, (p^6 + 5)/6, (p^8 + 5)/6 and (p^10 + 5)/6 are all prime.

Original entry on oeis.org

184279409, 619338131, 913749803, 1057351301, 1507289869, 1600204213, 2845213937, 4725908767, 4760956439, 5374709801, 5518707641, 8724256757, 9044067313, 9387396269, 10992352517, 11937043567, 13493126359, 13593105793, 17891702891, 17897035213, 17954907767, 19690938161, 20227580927, 20922685813, 21313027583, 21717176851
Offset: 1

Views

Author

Zak Seidov, Jan 20 2015

Keywords

Comments

The sequence contains all terms up to 10^10. There are no terms as yet for which (p^12 + 5)/6 is also prime.
No terms < 10^11 with (p^12 + 5)/6 prime. - Chai Wah Wu, Jan 27 2015

Links

Crossrefs

Subsequence of A253976.
Cf. A118915, A247478, A253925, A253940.

Programs

  • PARI
    lista(nn) = forprime(p=5, nn, if(ispseudoprime((p^2 + 5)/6) && ispseudoprime((p^4 + 5)/6) && ispseudoprime((p^6 + 5)/6) && ispseudoprime((p^8 + 5)/6) && ispseudoprime((p^10 + 5)/6), print1(p, ", "))); \\ Jinyuan Wang, Mar 01 2020
  • Python
    from gmpy2 import is_prime, t_divmod
A253941_list = []
for p in range(1,10**6,2):
    if is_prime(p):
        p2, x = p**2, 1
        for i in range(5):
            x *= p2
            q, r = t_divmod(x+5,6)
            if r or not is_prime(q):
                break
        else:
            A253941_list.append(p) # Chai Wah Wu, Jan 22 2015

Extensions

a(15)-a(26) from Chai Wah Wu, Jan 22 2015

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

A253939 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6 and (p^6 + 5)/6 are prime.

Original entry on oeis.org

7309, 45361, 67103, 97777, 128521, 149381, 374669, 543313, 656459, 872747, 940913, 1110817, 1219877, 1288603, 1324567, 1599319, 1629809, 2006677, 2129527, 2495501, 2544121, 2735839, 2763053, 2786363, 2856167, 3145661, 3428839, 3585149, 4063877, 4115971
Offset: 1

Views

Author

Zak Seidov, Jan 20 2015

Keywords

Links

Crossrefs

Subsequence of A253925. Cf. A118915, A247478.

Programs

  • Magma
    [p: p in PrimesUpTo(10^7) | IsPrime((p^2+5) div 6) and IsPrime((p^4+5) div 6) and IsPrime((p^6+5) div 6)]; // Vincenzo Librandi, Jan 21 2015
  • Mathematica
    Select[Prime[Range[10^7]], PrimeQ[(#^2 + 5) / 6] &&PrimeQ[(#^4 + 5) / 6] &&PrimeQ[(#^6 + 5) / 6] &] (* Vincenzo Librandi, Jan 21 2015 *)
Select[Prime[Range[3*10^5]],AllTrue[(#^{2,4,6}+5)/6,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 10 2016 *)
Showing 1-5 of 5 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.