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.

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A263310 Numbers n such that p=6*n+1, q=6*p+1 and r=6*q+1 are primes.

Original entry on oeis.org

10, 25, 55, 61, 101, 125, 156, 220, 221, 381, 391, 465, 475, 495, 576, 810, 891, 901, 975, 1060, 1145, 1396, 1430, 1630, 1650, 1726, 1795, 1811, 1881, 1885, 1915, 2196, 2265, 2335, 2391, 2405, 2456, 2536, 2575, 2636, 2651, 2820, 2911, 2915, 2951, 2965, 3051, 3211, 3245, 3335
Offset: 1

Views

Author

Zak Seidov, Oct 13 2015

Keywords

Comments

Subsequence of A263309 (and as such also of A024899).

Crossrefs

Cf. A024899, A263309.

Programs

  • Maple
    isA263310 := proc(n)
    return isprime(6*n+1) and isprime(36*n+7) and isprime(216*n+43) ;
end proc:
for n from 1 to 3000 do
    if isA263310(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Oct 17 2015
  • Mathematica
    Select[Range[10000],PrimeQ[p=6*#+1]&& PrimeQ[q=6*p+1]&& PrimeQ[r=6*q+1]&]
  • PARI
    for(n=1, 1e4, if(isprime(p=6*n+1)&&isprime(q=6*p+1)&&isprime(6*q+1), print1(n", "))) \\ Altug Alkan, Oct 17 2015

A263311 Numbers n such that each of p=6*n+1, q=6*p+1, r=6*q+1 and s=6*r+1 is prime.

Original entry on oeis.org

10, 1060, 1795, 1885, 2965, 3245, 3335, 4065, 4325, 5015, 5875, 6985, 7605, 7905, 9785, 11315, 12045, 12360, 14390, 14970, 15285, 15500, 15885, 17195, 18220, 20670, 20695, 22160, 24915, 25645, 25955, 26025, 29410, 29910, 32925, 35530, 36280
Offset: 1

Views

Author

Zak Seidov, Oct 13 2015

Keywords

Comments

Each p is a starting prime of a complete generalized Cunningham chain p(k)=6*p(k-1)+1.
All terms are multiples of 5. Hence t = 6s+1 = 1555+7776n are always composite, and the chains are indeed "complete."
Subsequence of A263310 (and as such of A263309 and of A024899).

Links

Crossrefs

Cf. A024899, A263309, A263310.

Programs

  • Maple
    isA263311 := proc(n)
    return isprime(6*n+1) and isprime(36*n+7) and isprime(216*n+43) and isprime(1296*n+259) ;
end proc:
for n from 1 to 30000 do
    if isA263311(n) then
        printf("%d,",n);
    end if;
end do; # R. J. Mathar, Oct 17 2015
  • Mathematica
    Select[Range[10,100000,5],PrimeQ[p=6*#+1]&&PrimeQ[q=6*p+1]&&PrimeQ[r=6*q+1]&&PrimeQ[s=6*r+1]&]
  • PARI
    for(n=1, 1e5, if(isprime(p=6*n+1) && isprime(q=6*p+1) && isprime(r=6*q+1) && isprime(6*r+1), print1(n", "))) \\ Altug Alkan, Oct 17 2015
Showing 1-2 of 2 results.

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

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