A242165 Smallest k>=0, such that n+/-k are both Fermi-Dirac primes (A050376).

0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 2, 0, 0, 1, 0, 3, 2, 3, 0, 1, 0, 3, 2, 3, 0, 1, 0, 9, 4, 3, 6, 5, 0, 9, 2, 3, 0, 1, 0, 3, 2, 3, 0, 1, 0, 3, 2, 9, 0, 5, 6, 3, 4, 9, 0, 1, 0, 9, 4, 3, 6, 5, 0, 15, 2, 3, 0, 1, 0, 7, 4, 3, 4, 5, 0, 1, 0, 1, 0, 5, 4, 3, 14, 9, 0, 7, 10, 9, 4, 13, 6, 7, 0

Offset: 2

Author

Vladimir Shevelev, May 05 2014

Keywords

• nonn

Comments

The existence of a(n)>=0 for all n >= 2 is equivalent to the Goldbach conjecture in Fermi-Dirac arithmetic (cf. comment in A241927) that every even number >= 4 is a sum of two terms of A050376 (it is slightly weaker than Goldbach conjecture for primes).

References

• V. S. Shevelev, Multiplicative functions in the Fermi-Dirac arithmetic, Izvestia Vuzov of the North-Caucasus region, Nature sciences 4 (1996), 28-43 (in Russian; MR 2000f: 11097, pp. 3912-3913).

Links

• Peter J. C. Moses, Table of n, a(n) for n = 2..10001

Crossrefs

Cf. A082467, A241922, A241927, A241947.

Formula

a(A050376(n)) = 0.