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
Examples
See A331259.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
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 -
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)
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