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A138716
Primes p2 such that p1^2 + p2^3 is an average of twin primes and p1 < p2 are consecutive primes.
4
29, 107, 1481, 1613, 2393, 2879, 4421, 5021, 5519, 5573, 6269, 7817, 8447, 9629, 11489, 11981, 12011, 17159, 17573, 18461, 19961, 21713, 23021, 23291, 23747, 24917, 26339, 27947, 29021, 29201, 29663, 30893, 32063, 32717, 34217, 34589, 35159, 36527, 36899, 44753
OFFSET
1,1
LINKS
EXAMPLE
29 is a term since 23 and 29 are consecutive primes, 23^2 + 29^3 = 24918, and (24917, 24919) are twin primes.
MATHEMATICA
a={}; Do[p1=Prime[n]; p2=Prime[n+1]; pp=p1^2+p2^3; If[PrimeQ[pp-1]&&PrimeQ[pp+1], AppendTo[a, p2]], {n, 16^3}]; Print[a];
Select[Partition[Prime[Range[5000]], 2, 1], AllTrue[#[[1]]^2+#[[2]]^3+{1, -1}, PrimeQ]&] [[All, 2]] (* Harvey P. Dale, Oct 29 2022 *)
PROG
(Magma) [NthPrime(k+1):k in [1..5000]| IsPrime(q-1) and IsPrime(q+1) where q is NthPrime(k)^2+ NthPrime(k+1)^3]; // Marius A. Burtea, Dec 22 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Amiram Eldar, Dec 22 2019
STATUS
approved