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A138755
Primes p2 such that p1^3 + p2^2 is an average of twin primes and p1 < p2 are consecutive primes.
6
29, 2081, 2357, 3373, 3727, 4013, 4093, 5233, 6007, 7829, 15559, 15797, 16319, 17123, 18523, 20143, 22037, 23071, 25261, 26293, 28019, 28289, 33797, 39499, 41627, 42181, 42929, 45121, 48533, 48823, 49123, 50417, 52697, 54629, 57973, 58897, 60887, 62761, 64381
OFFSET
1,1
LINKS
EXAMPLE
29 is a term since 23 and 29 are consecutive primes, 23^3 + 29^2 = 13008, and (13007, 13009) are twin primes.
MATHEMATICA
a={}; Do[p1=Prime[n]; p2=Prime[n+1]; pp=p1^3+p2^2; If[PrimeQ[pp-1]&&PrimeQ[pp+1], AppendTo[a, p2]], {n, 16^3}]; Print[a];
Select[Partition[Prime[Range[6500]], 2, 1], AllTrue[#[[1]]^3+#[[2]]^2+{1, -1}, PrimeQ]&][[All, 2]] (* Harvey P. Dale, Aug 29 2021 *)
PROG
(Magma) [NthPrime(k+1):k in [1..7000]| IsPrime(q-1) and IsPrime(q+1) where q is NthPrime(k)^3+ NthPrime(k+1)^2]; // Marius A. Burtea, Dec 22 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Amiram Eldar, Dec 22 2019
STATUS
approved