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A258233 Number of ways to represent the n-th prime as arithmetic mean of three other primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A047556 A255053 A292762 * A015819 A298794 A181683

Adjacent sequences:  A258230 A258231 A258232 * A258234 A258235 A258236

KEYWORD

nonn

AUTHOR

Zak Seidov, May 24 2015

STATUS

approved

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Last modified May 21 08:53 EDT 2019. Contains 323441 sequences. (Running on oeis4.)