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

1,4

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).

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A000040, A071703, A071704.

Sequence in context: A292762 A374845 A364927 * A015819 A298794 A181683

Adjacent sequences: A258230 A258231 A258232 * A258234 A258235 A258236

Keyword

nonn

Author

Zak Seidov, May 24 2015

Status

approved