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

%I A261748 #12 Sep 08 2022 08:46:13
%S A261748 19081,17569,124561,284129,461933,12994939,59888791,136812059,
%T A261748 210687859,381287213,430477739,967646789,1003292441,1214844443,
%U A261748 1235842577,1630956673,2035265203,3409511489,3760252651,4212399799,5010219631,5823581399,6487158329,7774729381,8729833339
%N A261748 Primes of the form p^3 - q^3 + r^3 where p, q, r are consecutive primes.
%C A261748 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
%H A261748 K. D. Bajpai, <a href="/A261748/b261748.txt">Table of n, a(n) for n = 1..10000</a>
%e A261748 19081 appears in the sequence because 19^3 - 23^3 + 29^3 = 19081 which is prime and 19, 23, 29 are consecutive primes.
%e A261748 17569 appears in the sequence because 23^3 - 29^3 + 31^3 = 17569 which is prime and 23, 29, 31 are consecutive primes.
%t A261748 Select[Table[(Prime[n]^3 - Prime[n + 1]^3 + Prime[n + 2]^3), {n, 1, 1000}], PrimeQ]
%t A261748 Select[#[[1]]-#[[2]]+#[[3]]&/@Partition[Prime[Range[500]]^3,3,1],PrimeQ] (* _Harvey P. Dale_, Jul 29 2021 *)
%o A261748 (PARI) for(n=1, 500, k=(prime(n)^3 - prime(n+1)^3 + prime(n+2)^3 ); if(isprime(k), print1(k, ", ")));
%o A261748 (Magma) [k: n in [1..1000] | IsPrime(k) where k is (NthPrime(n)^3 - NthPrime(n+1)^3 + NthPrime(n+2)^3)];
%Y A261748 Cf. A000040, A000578, A030078, A164129, A165612.
%K A261748 nonn
%O A261748 1,1
%A A261748 _K. D. Bajpai_, Aug 30 2015