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A178670
Number of ways to express prime(n) as (prime(n+k) + prime(n-k))/2.
6
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
1,5
EXAMPLE
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.
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}]
PROG
(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}
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved