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A242165 Smallest k>=0, such that n+/-k are both Fermi-Dirac primes (A050376). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 22 17:18 EDT 2021. Contains 345388 sequences. (Running on oeis4.)