A178670 Number of ways to express prime(n) as (prime(n+k) + prime(n-k))/2.

0, 0, 1, 0, 2, 1, 1, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 1, 3, 0, 0, 1, 1, 2, 1, 1, 1, 0, 0, 2, 2, 2, 1, 0, 1, 3, 0, 1, 3, 2, 1, 4, 2, 1, 0, 4, 0, 0, 0, 2, 0, 0, 2, 1, 1, 0, 0, 1, 0, 0, 0, 3, 4, 0, 0, 1, 1, 1, 2, 3, 3, 2, 4, 2, 2, 1, 3, 4, 4, 1, 1, 1, 3, 2, 2, 2, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 3, 0, 2

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 04 2011

Keywords

• nonn

Examples

			a(5) = 2 because the 5th prime (11) is half the sum of the 7th and 3rd prime (17+5) or half the sum of the 8th and 2nd prime (19+3).
a(8) = 0 because the 8th prime (19) cannot be expressed as (1/2)*(prime(8+k) + prime(8-k)) for any k.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A129363, A178609, A178954.

Programs

Mathematica

nn=1000; p=Prime[Range[2*nn]]; Table[s=Take[p,n-1] + Reverse[Take[p, {n+1,2n-1}]]; Count[s,2*p[[n]]], {n,nn}]

PARI

a(n)={s=2*prime(n);a=0;for(i=1,n-1,if(prime(n+i)+prime(n-i)==s,a=a+1));a}