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.

A224610 Smallest j such that j*2*prime(n)^3-1 and j*2*prime(n)*q^2-1 are prime.

Original entry on oeis.org

2, 2, 5, 7, 59, 142, 264, 25, 8, 21, 124, 33, 60, 87, 9, 231, 5, 6, 82, 155, 7, 66, 72, 21, 42, 105, 15, 48, 250, 68, 222, 54, 47, 195, 255, 360, 205, 6, 83, 26, 5, 1, 50, 220, 173, 1, 976, 30, 228, 130, 30, 129, 46, 1106, 65, 62, 15, 109, 24, 41, 922, 15, 132, 89
Offset: 1

Views

Author

Pierre CAMI, Apr 12 2013

Keywords

Links

Crossrefs

Cf. A224490, A224609, A224611, A224612.

Programs

  • Mathematica
    a[n_] := For[p = Prime[n]; j = 1, j < 10^6, j++, If[PrimeQ[q = j*2*p^3 - 1] && PrimeQ[j*p*2*q^2 - 1], Return[j]]]; Table[a[n], {n, 1, 75}] (* Jean-François Alcover, Apr 22 2013 *)

A224612 Let p = prime(n). Smallest j such that q = j*2*p^3-1, r = j*p*2*q^2-1, s = j*p*2*r^2-1, and j*p*2*s^2-1 are prime numbers.

Original entry on oeis.org

29952, 12063, 1463, 6102, 11661, 49552, 639179, 2099290, 291248, 393186, 545251, 321303, 436641, 278295, 746832, 237852, 56490, 165901, 152847, 619755, 777177, 3410085, 117513, 2015421, 497170, 14750, 161190, 347039, 251835, 57536, 222, 2083286, 384944, 1228474, 3909960, 344164, 332224, 207751, 14060
Offset: 1

Views

Author

Pierre CAMI, Apr 12 2013

Keywords

Comments

Conjecture: a(n) exists for all n.

Crossrefs

Cf. A224492, A224609, A224610, A224611.

Programs

  • Maple
    f:= proc(n) local j,p,q,r,s;
    p:= ithprime(n);
    for j from 1 do
      q:= j*2*p^3-1; if not isprime(q) then next fi;
      r:= j*p*2*q^2-1; if not isprime(r) then next fi;
      s:= j*p*2*r^2-1; if not isprime(s) then next fi;
      if isprime(j*p*2*s^2-1) then return j fi;
    od
end proc;
map(f, [$1..25]); # Robert Israel, May 15 2025
  • Mathematica
    a[n_] := For[j = 1, j < 10^7, j++, p = Prime[n]; If[PrimeQ[q = j*2*p^3 - 1] && PrimeQ[r = j*2*p*q^2 - 1] && PrimeQ[s = j*2*p*r^2 - 1] && PrimeQ[j*2*p*s^2 - 1], Return[j]]]; Table[Print[an = a[n]]; an, {n, 1, 24}] (* Jean-François Alcover, Apr 12 2013 *)

Extensions

More terms from Jean-François Alcover, Apr 12 2013
Name clarified and more terms from Robert Israel, May 15 2025

A224626 Primes p such that q=2*p^3-1, r=2*p*q^2-1, and s=2*p*r^2-1 are all prime.

Original entry on oeis.org

27361, 65731, 167623, 424093, 1559449, 2389693, 3880633, 4683661, 5755921, 5780881, 6124411, 6840643, 7802959, 7822879, 7917769, 8876719, 9488683, 9640321, 9966139, 10392073, 10865083, 10988743, 12363991, 12457681, 12756253, 13471561, 14437561, 14508709, 14550331, 14839711, 15366223, 16574143
Offset: 1

Views

Author

Pierre CAMI, Apr 12 2013

Keywords

Comments

A prime p here is prime p(n) when A224611(n) = 1.
A subsequence of A224614. - M. F. Hasler, Apr 22 2013

Links

Crossrefs

Cf. A224611, A224613, A224614.

Programs

  • Mathematica
    Reap[ For[p = 2, p < 2*10^7, p = NextPrime[p], If[PrimeQ[q = 2*p^3 - 1] && PrimeQ[r = 2*p*q^2 - 1] && PrimeQ[2*p*r^2 - 1], Print[p]; Sow[p]] ]][[2, 1]] (* Jean-François Alcover, Apr 22 2013 *)
apQ[n_]:=Module[{q=2n^3-1,r},r=2n q^2-1;And@@PrimeQ[{q,r,2n r^2-1}]]; Select[ Prime[Range[1100000]],apQ] (* Harvey P. Dale, Nov 24 2013 *)
Showing 1-3 of 3 results.

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

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