A258233 Number of ways to represent the n-th prime as arithmetic mean of three other primes.

0, 1, 1, 3, 6, 7, 11, 15, 16, 25, 30, 32, 42, 40, 44, 52, 63, 71, 76, 87, 82, 97, 102, 113, 127, 137, 136, 143, 154, 154, 186, 200, 204, 215, 234, 249, 251, 262, 272, 284, 309, 324, 345, 334, 349, 359, 406, 414, 431, 447, 441, 489, 487, 511, 508

Offset: 1

Author

Zak Seidov, May 24 2015

Keywords

• nonn

Comments

Differs from A071704: for n>1, if 3*prime(n)-4 is prime then a(n)=1+A071704(n), otherwise a(n)=A071704(n).

Examples

			a(5)=6 as A000040(5)=11 and  11 has 6 representations  as arithmetic mean of three other (not equal to 11) primes:
11 = (2+2+29)/3=(3+7+23)/3 = (3+13+17)/3 = (5+5+23)/3 = (7+7+19)/3 = (7+13+13)/3.
		

Links

• Zak Seidov and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Seidov)

Crossrefs

Cf. A000040, A071703, A071704.

Programs

PARI

a(n,p=prime(n))=my(s=0); forprime(q=p+2,3*p-4, my(t=3*p-q); forprime(r=max(t-q, 2),(3*p-q)\2, if(t!=p+r && isprime(t-r), s++))); s \\ Charles R Greathouse IV, Jun 04 2015