This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
If the primes 2 through 13 are split into equal-sized sets, the larger product of the two is not less than 182. This is the value for {2, 7, 13}, so a(3)=182.
{
p=vector(50,n,prime(n));i=1;
while(1,
P=prod(j=1,2*i,p[j]);Q=sqrt(P);r=10^1000;
m=prod(j=1,i,p[j]);a=vectorsmall(2*i-1);
for(j=1,i,a[j]=1);b=vectorsmall(2*i-1);
for(j=i,2*i-1,b[j]=1);while(1,
if(m>Q,if(m
For n = 1, two distinct fractions can be written with the first prime number, namely 1/2 and 2. Of the two, 1/2 is nearer to 1. 1/2 has its 2 below the fraction bar, so its binary encoding is 0, which yields a(1) = 0. For n = 2, four distinct fractions can be written with the first two prime numbers, namely 1/6, 2/3, 3/2 and 6. 2/3 is the nearest to 1. 2/3 has its 2 above the fraction bar and its 3 below, so its encoding is 01, which yields a(2) = 1.
package oeis;
public class BinaryEncodedBestPrimeSetup {
// Brute force implementation... Can it be improved?
public static int PRIME[] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, /* to be continued */ };
public static void main(String args[]) {
int nMax = PRIME.length; // number of terms of the sequence
for (int n = 1; n <= nMax; n ++) {
if (n > 1) {
System.out.print(", ");
}
System.out.print(u(n));
}
}
private static int u(int n) {
double bestMul = 0.0;
int bestSetup = -1;
int s = 0; // binary-encoded setup number
for (s = 0; s < (1 << n); s ++) {
double mul = 1.0;
int i = 0; // prime number #
for (i = 0; i < n; i ++) {
if ((s & (1 << i)) != 0) {
mul *= PRIME[i]; // 1 = above fraction bar
} else {
mul /= PRIME[i]; // 0 = below fraction bar
}
}
if (mul < 1.0) {
if (mul > bestMul) {
bestMul = mul;
bestSetup = s;
}
}
}
return bestSetup;
}
}
{0}~Join~Table[Function[p, FromDigits[#, 2] &@ Reverse@ MapAt[# + 1 &, ConstantArray[0, n], Partition[#, 1, 1]] &@ PrimePi@ FactorInteger[Numerator@ #][[All, 1]] &@ Max@ Select[Map[p/#^2 &, Divisors@ p], # < 1 &]][Times @@ Prime@ Range@ n], {n, 2, 23}] (* Michael De Vlieger, Oct 19 2016 *)
a060795(n) = my(m=prod(i=1, n, prime(i))); divisors(m)[numdiv(m)\2];
a(n) = {my(a95 = a060795(n)); v = vector(n, i, (a95 % prime(i))==0); subst(Polrev(v), x, 2); } \\ Michel Marcus, Dec 03 2016
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