A224614 -id:A224614 - cp's OEIS frontend

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

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

Pierre CAMI, Apr 12 2013

nonn

A prime p here is prime p(n) when A224611(n) = 1.

A subsequence of A224614. - M. F. Hasler, Apr 22 2013

Pierre CAMI, Table of n, a(n) for n = 1..747

Cf. A224611, A224613, A224614.

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 *)

A224990 Primes p such that q = 2p^2 - 1 and 2p*q - 1 are also prime.

Original entry on oeis.org

3, 13, 157, 181, 739, 829, 937, 1009, 1093, 1483, 1621, 1879, 2311, 2503, 2647, 2719, 3079, 4969, 4999, 5209, 5431, 5569, 6163, 6961, 8161, 8329, 9349, 9631, 10399, 10459, 10531, 10657, 11131, 11953, 13063, 18523, 20149, 20731, 21391, 21589, 26317, 27481, 28111, 28351, 29023

Offset: 1

M. F. Hasler, Apr 22 2013

nonn

Subsequence of A106483, and more elementary version of A224614.

Select[Prime[Range[10000]], PrimeQ[2#^2 - 1] && PrimeQ[4#^3 - 2# - 1] &] (* Alonso del Arte, Apr 22 2013 *)

forprime(p=1,3e4,isprime(r=2*p^2-1)&&isprime(2*p*r-1)&&print1(p","))

A224627 Prime numbers p such that 2p^3-1, 2p*q^2-1, 2pr^2-1, and 2ps^2-1 are prime numbers.

Original entry on oeis.org

19460899, 86276401, 87980803, 167646631, 300722029, 343507111, 479516311, 906597943, 998757829, 1031308249, 1112697199, 1311383431, 1962194053

Offset: 1

Pierre CAMI, Apr 12 2013

nonn

Subsequence of A224612, p = prime(n) when A224612(n)=1.

Cf. A224612, A224613, A224614, A224626.

Reap[ For[p = 2, p < 2*10^9, p = NextPrime[p], If[PrimeQ[q = 2*p^3 - 1] && PrimeQ[r = 2*p*q^2 - 1] && PrimeQ[s = 2*p*r^2 - 1] && PrimeQ[2*p*s^2 - 1], Print[p]; Sow[p]] ]][[2, 1]] (* Jean-François Alcover, Apr 22 2013 *)

More terms from Jean-François Alcover, Apr 22 2013

cp's OEIS Frontend

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

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A224990 Primes p such that q = 2p^2 - 1 and 2p*q - 1 are also prime.

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PARI

A224627 Prime numbers p such that 2p^3-1, 2p*q^2-1, 2pr^2-1, and 2ps^2-1 are prime numbers.

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cp's OEIS Frontend

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.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A224990 Primes p such that q = 2*p^2 - 1 and 2*p*q - 1 are also prime.

Views

Author

Keywords

Comments

Programs

Mathematica

PARI

A224627 Prime numbers p such that 2*p^3-1, 2*p*q^2-1, 2*p*r^2-1, and 2*p*s^2-1 are prime numbers.

Views

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Mathematica

Extensions

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

A224990 Primes p such that q = 2p^2 - 1 and 2p*q - 1 are also prime.

A224627 Prime numbers p such that 2p^3-1, 2p*q^2-1, 2pr^2-1, and 2ps^2-1 are prime numbers.