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
Keywords
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
Programs
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Magma
[k: n in [1..1000] | IsPrime(k) where k is (NthPrime(n)^3 - NthPrime(n+1)^3 + NthPrime(n+2)^3)];
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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, ", ")));
Comments