A261748 Primes of the form p^3 - q^3 + r^3 where p, q, r are consecutive primes.

19081, 17569, 124561, 284129, 461933, 12994939, 59888791, 136812059, 210687859, 381287213, 430477739, 967646789, 1003292441, 1214844443, 1235842577, 1630956673, 2035265203, 3409511489, 3760252651, 4212399799, 5010219631, 5823581399, 6487158329, 7774729381, 8729833339

Offset: 1

Author

K. D. Bajpai, Aug 30 2015

Keywords

• nonn

Comments

Indices of the initial primes p: 8, 9, 14, 18, 20, 51, 76, 96, 108, 128, 133, 166, 168, ..., . - Robert G. Wilson v, Sep 03 2015

Examples

			19081 appears in the sequence because 19^3 - 23^3 + 29^3 = 19081 which is prime and 19, 23, 29 are consecutive primes.
17569 appears in the sequence because 23^3 - 29^3 + 31^3 = 17569 which is prime and 23, 29, 31 are consecutive primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000578, A030078, A164129, A165612.

Programs

Magma

[k: n in [1..1000] | IsPrime(k) where k is (NthPrime(n)^3 - NthPrime(n+1)^3 + NthPrime(n+2)^3)];

Mathematica

Select[Table[(Prime[n]^3 - Prime[n + 1]^3 + Prime[n + 2]^3), {n, 1, 1000}], PrimeQ]
Select[#[[1]]-#[[2]]+#[[3]]&/@Partition[Prime[Range[500]]^3,3,1],PrimeQ] (* Harvey P. Dale, Jul 29 2021 *)

PARI

for(n=1, 500, k=(prime(n)^3 - prime(n+1)^3 + prime(n+2)^3 ); if(isprime(k), print1(k, ", ")));