A138755 Primes p2 such that p1^3 + p2^2 is an average of twin primes and p1 < p2 are consecutive primes.
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
Keywords
Examples
29 is a term since 23 and 29 are consecutive primes, 23^3 + 29^2 = 13008, and (13007, 13009) are twin primes.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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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
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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 *)
Extensions
More terms from Amiram Eldar, Dec 22 2019