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A331259 Numerator of harmonic mean of 3 consecutive primes. Denominators are A331260. 1
90, 315, 1155, 3003, 7293, 12597, 22287, 38019, 62031, 99789, 141081, 195693, 248583, 321339, 146969, 572241, 723399, 870531, 1041783, 1228371, 1435983, 1750719, 2149617, 2615799, 3027273, 3339363, 3603867, 3953757, 4692777, 5639943, 6837807, 7483899, 8512221 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..33.

FORMULA

a(n) = numerator ((3*p1*p2*p3)/(p2*p3 + p1*p3 + p1*p2)) with p1 = prime(n), p2 = prime(n + 1), p3 = prime(n + 2).

EXAMPLE

b(1) = a(1)/A331260(1) = 3*2*3*5 / (3*5 + 2*5 + 2*3) = 90/31,

b(2) = a(2)/A331260(2) = 3*3*5*7 / (5*7 + 3*7 + 3*5) = 315/71,

...

b(15) = a(15)/A331260(15) = 3*47*53*59 / (53*59 + 47*59 + 47*53) = 440907/8391 = 146969/2797. The common factor of 3 (see A292530) makes the denominator different from A127345(15).

PROG

(PARI) hm3(x, y, z)=3/(1/x+1/y+1/z);

p1=2; p2=3; forprime(p3=5, 150, print1(numerator(hm3(p1, p2, p3)), ", "); p1=p2; p2=p3)

CROSSREFS

Cf. A046301, A127345, A292530, A331260.

Sequence in context: A250877 A250878 A027621 * A245866 A157888 A201103

Adjacent sequences:  A331256 A331257 A331258 * A331260 A331261 A331262

KEYWORD

nonn,frac

AUTHOR

Hugo Pfoertner, Jan 19 2020

STATUS

approved

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Last modified October 24 20:01 EDT 2020. Contains 338009 sequences. (Running on oeis4.)