

A317595


a(n) is the number of primes between 2n and the largest prime p such that 2np is also a prime.


1



1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 3, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0
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OFFSET

2,48


COMMENTS

If the Goldbach Conjecture is true, this sequence is defined for n >= 2.


LINKS

Table of n, a(n) for n=2..88.
Index entries for sequences related to Goldbach conjecture


FORMULA

a(n) = A000720(A020482(n))  A020482(2*n).  Michel Marcus, Aug 02 2018


EXAMPLE

For n=2, 2n=4 = 2+2, there is one prime, which is 3, between 2 and 4. So a(2)=1;
...
For n=8, 2n=16 = 13+3, there is no prime between 13 and 16. So a(8)=0;
...
For n=49, 2n=98 = 79+19, there are three primes, 83, 89, and 97 between 79 and 98 such that the difference of 98 and these primes, 15, 9, and 1 respectively, are not prime. So a(49)=3.


MATHEMATICA

Table[n2 = n*2; p = NextPrime[n2]; ct = 0; While[p = NextPrime[p, 1]; ! PrimeQ[n2  p], ct++]; ct, {n, 2, 88}]


CROSSREFS

Cf. A000040, A000720, A002375, A020482.
Sequence in context: A307808 A200472 A309887 * A263753 A303877 A112743
Adjacent sequences: A317592 A317593 A317594 * A317596 A317597 A317598


KEYWORD

nonn,easy


AUTHOR

Lei Zhou, Aug 01 2018


STATUS

approved



