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A258233
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Number of ways to represent the n-th prime as arithmetic mean of three other primes.
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4
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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
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OFFSET
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1,4
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COMMENTS
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Differs from A071704: for n>1, if 3*prime(n)-4 is prime then a(n)=1+A071704(n), otherwise a(n)=A071704(n).
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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