login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A291374 Primes p such that p^3*q^3 + p + q is prime, where q is next prime after p. 2
11, 17, 41, 43, 47, 137, 313, 359, 389, 401, 491, 557, 577, 709, 757, 829, 863, 929, 937, 953, 1129, 1163, 1249, 1301, 1307, 1439, 1597, 1627, 1693, 1847, 2087, 2311, 2351, 2437, 2663, 2731, 2741, 3109, 3119, 3217, 3253, 4027, 4219, 4271, 4547, 4637, 5189, 5237 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 11 is prime; 13 is the next prime: 11^3*13^3 + 11 + 13 = 1331*2197 + 11 + 13 = 2924231 that is a prime.

a(2) = 17 is prime; 19 is the next prime: 17^3*19^3 + 17 + 19 = 4913*6859 + 17 + 19 = 33698303 that is a prime.

MAPLE

select(p -> andmap(isprime, [p, (p^3*nextprime(p)^3+p+nextprime(p))]), [seq(p, p=1..10^4)]);

MATHEMATICA

Prime@Select[Range[1000], PrimeQ[Prime[#]^3* Prime[# + 1]^3 + Prime[#] + Prime[# + 1]] &]

PROG

(PARI) forprime(p=1, 5000, q=nextprime(p+1); if(ispseudoprime(p^3*q^3 + p + q), print1(p, ", ")));

(PARI) list(lim)=my(v=List(), p=2, p3=8, q3); forprime(q=3, nextprime(lim\1+1), q3=q^3; if(isprime(p3*q3+p+q), listput(v, p)); p=q; p3=q3); Vec(v) \\ Charles R Greathouse IV, Aug 23 2017

(MAGMA) [p: p in PrimesUpTo(5000) | IsPrime(p^3*q^3 + p + q) where q is NextPrime(p)];

CROSSREFS

Cf. A000040, A001043, A006094, A030078, A096342, A120398, A126148, A152241, A291339.

Sequence in context: A317678 A098649 A078872 * A181421 A290530 A163387

Adjacent sequences:  A291371 A291372 A291373 * A291375 A291376 A291377

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Aug 23 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 12 05:33 EDT 2020. Contains 336438 sequences. (Running on oeis4.)