Problems & Puzzles: Puzzles
Puzzle 261. Symmetric prime constellations
Someone named 'Dale' submitted the following curio to the well know Prime Curios! pages:
That is to say, 18731, is at the 'center' of the following symmetrically spaced consecutive primes:
18713, 18719, 18731, 18743, 18749
such that 18731 = (18719+18743)/2=(18713+18749)/2
I have generalized this and ask for the earliest prime such that it is the average of its k-th immediate consecutive prime neighbors, for k=1 to m, for m=1, 2, 3, .... The Dale's example is the solution for m=2.
The sequence of these earlier primes goes like this: 5, 18731, 683783, 98303927, ... (?)
Question: Find more terms to this sequence.
Faride Firoozbakht and J. K. Andersen found that the 5th term of this sequence was already discovered by Jud McCranie and reported in the EIS sequence A055380.
So the first real unknown term is the 6th one.
Giovanni Resta found it! (October, 2004):