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A158526 n and (1 + 2*n + 2*n^2) are primes. 2

%I

%S 2,5,7,17,19,29,47,79,97,109,137,139,149,157,167,199,229,347,349,389,

%T 409,467,479,547,577,599,709,719,757,857,929,937,967,1039,1069,1087,

%U 1187,1229,1259,1399,1409,1447,1559,1579,1597,1607,1657,1697,1699,1709

%N n and (1 + 2*n + 2*n^2) are primes.

%C Numbers n such that A048395(n) is semiprime, or A048395(n)/n is prime.

%C Or, primes in A027861. Also, (1+2*n+2*n^2) are in A027862. - _Zak Seidov_, Sep 19 2015

%H Charles R Greathouse IV, <a href="/A158526/b158526.txt">Table of n, a(n) for n = 1..10000</a>

%e A048395(2)=26=2*13, A048395(5)=305=5*61, A048395(7)=791=7*113.

%t f[n_]:=PrimeQ[n^2+(n+1)^2];lst={};Do[p=Prime[n];If[f[p],AppendTo[lst,p]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 27 2009 *)

%o (PARI) forprime(p=2,1e4,if(isprime(2*p*(p+1)+1),print1(p","))) \\ _Charles R Greathouse IV_, Sep 09 2009

%o (MAGMA) [p: p in PrimesUpTo(2000) | IsPrime(2*p^2+2*p+1)]; // _Vincenzo Librandi_, Jun 22 2014

%Y Cf. A048395 (sum of consecutive nonsquares), A001358 (semiprimes).

%Y Cf. A027861, A027862.

%K nonn,easy

%O 1,1

%A _Zak Seidov_, Mar 20 2009

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Last modified May 19 17:08 EDT 2019. Contains 323395 sequences. (Running on oeis4.)