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URL: https://oeis.org/A331259

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A331259
Numerator of harmonic mean of 3 consecutive primes. Denominators are A331260.
2
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
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).
a(n) = p1*p2*p3 if p1 == p2 == p3 (mod 3), otherwise 3*p1*p2*p3. - Robert Israel, Jul 29 2024
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).
MAPLE
q:= proc(a, b, c) if nops({a, b, c} mod 3) = 1 then a*b*c else 3*a*b*c fi end proc:
P:= [seq(ithprime(i), i=1..102)]:
seq(q(P[i], P[i+1], P[i+2]), i=1..100); # Robert Israel, Jul 29 2024
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
KEYWORD
nonn,frac,look
AUTHOR
Hugo Pfoertner, Jan 19 2020
STATUS
approved