A331260 - OEIS

%I #11 Jul 29 2024 06:20:29

%S 31,71,167,311,551,791,1151,1655,2279,3119,3935,4871,5711,6791,2797,

%T 9959,11639,13175,14831,16559,18383,20975,24071,27419,30191,32231,

%U 33911,36071,40511,45791,51983,55199,60167,64199,69599,24637,79031,84311,29917,94679

%N Denominator of harmonic mean of 3 consecutive primes. Numerators are A331259.

%H Robert Israel, <a href="/A331260/b331260.txt">Table of n, a(n) for n = 1..10000</a>

%F 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).

%F 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

%e See A331259.

%p P:= [seq(ithprime(i),i=1..102)]:

%p 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;

%p [seq(f(P[i],P[i+1],P[i+2]),i=1..100)]; # _Robert Israel_, Jul 28 2024

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

%o p1=2; p2=3; forprime(p3=5, 190, print1(denominator(hm3(p1, p2, p3)), ", "); p1=p2; p2=p3)

%Y Cf. A046301, A127345, A292530, A331259.

%K nonn,frac,look

%O 1,1

%A _Hugo Pfoertner_, Jan 19 2020