A337489
a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-1..k+1} prime(j)/3) sets a new record.
Original entry on oeis.org
3, 7, 29, 113, 523, 1151, 1327, 9551, 15683, 19609, 25471, 31397, 156007, 360653, 370261, 492113, 1349533, 1357201, 1357333, 1562051, 2010733, 4652507, 17051707, 17051887, 20831323, 47326693, 47326913, 122164747, 189695893, 191912783, 387096133, 428045741, 436273291
Offset: 1
List of first terms:
a(n) pi(a(n)) average-median
3, 2, 1/3 = (2 + 3 + 5)/3 - 3
7, 4, 2/3 = (5 + 7 + 11)/3 - 7
29, 10, -4/3 = (23 + 29 + 31)/3 - 29
113, 30, 10/3
523, 99, 16/3
1151, 190, -20/3
1327, 217, 28/3
9551, 1183, 32/3
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a337489(limp) = {my(p1=0, p2=2, p3=3, s=p1+p2+p3, d=0); forprime(p=5, limp, s=s-p1+p; my(dd=abs(s/3-p3)); if(dd>d, print1(p3, ", "); d=dd); p1=p2; p2=p3; p3=p)};
a337489(500000000)
A331259
Numerator of harmonic mean of 3 consecutive primes. Denominators are A331260.
Original entry on oeis.org
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
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).
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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
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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)
A331260
Denominator of harmonic mean of 3 consecutive primes. Numerators are A331259.
Original entry on oeis.org
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
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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
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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)
Showing 1-3 of 3 results.
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