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

2,13

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

Formula

a(A050376(n)) = 0.

Crossrefs

Cf. A082467, A241922, A241927, A241947.

Sequence in context: A206825 A336551 A292380 * A231724 A214851 A245203

Adjacent sequences: A242162 A242163 A242164 * A242166 A242167 A242168

Keyword

nonn

Author

Vladimir Shevelev, May 05 2014

Status

approved