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A062718 p and p^2 + 6 are both prime. 9
5, 11, 19, 31, 61, 79, 89, 109, 131, 151, 199, 269, 331, 401, 431, 569, 709, 859, 929, 941, 971, 991, 1039, 1249, 1319, 1361, 1409, 1451, 1531, 1549, 1559, 1571, 1601, 1619, 1699, 1879, 1901, 1999, 2069, 2081, 2089, 2111, 2179, 2341, 2399, 2411, 2621 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Solutions of the equation n' + (n^2+6)' = 2, where n' is the arithmetic derivative of n. [Paolo P. Lava, Nov 09 2012]

The only common term with A137270 is 5. - Zak Seidov, Jun 16 2015

First cases of two, three and four consecutive primes are {2069,2081}, {3041,3049,3061} and {3403531,3403549,3403559,3403571}. - Zak Seidov, Jun 16 2015

LINKS

Harry J. Smith, Table of n, a(n) for n=1..1000

MATHEMATICA

f[n_]:=n^2+6; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 16 2009 *)

Select[Prime[Range[400]], PrimeQ[#^2 + 6] &] (* Vincenzo Librandi, Jun 16 2015 *)

PROG

(PARI) je=[]; for(n=1, 700, if(isprime(prime(n)^2+6), je=concat(je, prime(n)))); je

(PARI) { n=0; for (m=1, 10^9, if (isprime(prime(m)^2 + 6), write("b062718.txt", n++, " ", prime(m)); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 09 2009

(MAGMA) [p: p in PrimesUpTo(3000) |IsPrime(p^2+6)]; // Vincenzo Librandi, Jun 16 2015

CROSSREFS

Cf. A137270. - Zak Seidov, Jun 16 2015

Sequence in context: A065995 A023245 A125003 * A326123 A288112 A225250

Adjacent sequences:  A062715 A062716 A062717 * A062719 A062720 A062721

KEYWORD

nonn

AUTHOR

Jason Earls, Jul 14 2001

STATUS

approved

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Last modified April 5 20:24 EDT 2020. Contains 333260 sequences. (Running on oeis4.)