A331260 Denominator of harmonic mean of 3 consecutive primes. Numerators are A331259.

31, 71, 167, 311, 551, 791, 1151, 1655, 2279, 3119, 3935, 4871, 5711, 6791, 2797, 9959, 11639, 13175, 14831, 16559, 18383, 20975, 24071, 27419, 30191, 32231, 33911, 36071, 40511, 45791, 51983, 55199, 60167, 64199, 69599, 24637, 79031, 84311, 29917, 94679

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = denominator ((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 + p1*p3 + p2*p3)/3 if p1 == p2 == p3 (mod 3), otherwise p1*p2 + p1*p3 + p2*p3. - Robert Israel, Jul 29 2024

Example

See A331259.

Maple

P:= [seq(ithprime(i), i=1..102)]:
f:= proc(a, b, c) if nops({a, b, c} mod 3) = 1 then (a*b+a*c+b*c)/3 else a*b+a*c+b*c fi end proc;
[seq(f(P[i], P[i+1], P[i+2]), i=1..100)]; # Robert Israel, Jul 28 2024

Prog

(PARI) hm3(x, y, z)=3/(1/x+1/y+1/z);
p1=2; p2=3; forprime(p3=5, 190, print1(denominator(hm3(p1, p2, p3)), ", "); p1=p2; p2=p3)

Crossrefs

Cf. A046301, A127345, A292530, A331259.

Sequence in context: A356457 A139975 A050957 * A127345 A127346 A089704

Adjacent sequences: A331257 A331258 A331259 * A331261 A331262 A331263

Keyword

nonn,frac,look

Author

Hugo Pfoertner, Jan 19 2020

Status

approved