A331259 Numerator of harmonic mean of 3 consecutive primes. Denominators are A331260.

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

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