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- #!/usr/bin/perl
- # a(n) is the least k such that Sum_{i=1..k} (i/prime(i))^n > 1.
- # https://oeis.org/A343375
- # Known terms:
- # 2, 3, 6, 129, 107103, 19562634
- # New terms:
- # a(7) = 2433065908
- # Term a(7) double-checked with PARI/GP (took 1 hour to verify):
- # k = 2433065907 gives: 0.99999999993821766811733842990753602502
- # k = 2433065908 gives: 1.00000000017401085698940764192873576233
- use 5.014;
- use warnings;
- use ntheory qw(:all);
- my $k = 1;
- my $n = 7;
- my $sum = 0;
- forprimes {
- $sum += exp((log($k) - log($_))*$n);
- if ($sum >= 1) {
- die "a($n) = $k (with p = $_)\n";
- }
- ++$k;
- } 1e12;
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