Mian-Chowla sequence
The Mian–Chowla sequence is an integer sequence defined recursively.
The sequence starts with:
- a1 = 1
then for n > 1, an is the smallest positive integer such that every pairwise sum
- ai + aj
is distinct, for all i and j less than or equal to n.
- The Task
- Find and display, here, on this page the first 30 terms of the Mian–Chowla sequence.
- Find and display, here, on this page the 91st through 100th terms of the Mian–Chowla sequence.
Demonstrating working through the first few terms longhand:
- a1 = 1
- 1 + 1 = 2
Speculatively try a2 = 2
- 1 + 1 = 2
- 1 + 2 = 3
- 2 + 2 = 4
There are no repeated sums so 2 is the next number in the sequence.
Speculatively try a3 = 3
- 1 + 1 = 2
- 1 + 2 = 3
- 1 + 3 = 4
- 2 + 2 = 4
- 2 + 3 = 5
- 3 + 3 = 6
Sum of 4 is repeated so 3 is rejected.
Speculatively try a3 = 4
- 1 + 1 = 2
- 1 + 2 = 3
- 1 + 4 = 5
- 2 + 2 = 4
- 2 + 4 = 6
- 4 + 4 = 8
There are no repeated sums so 4 is the next number in the sequence.
And so on...
- See also
Go
<lang go>package main
import "fmt"
func contains(is []int, s int) bool {
for _, i := range is { if s == i { return true } } return false
}
func mianChowla(n int) []int {
mc := make([]int, n) mc[0] = 1 is := []int{2} var sum int for i := 1; i < n; i++ { le := len(is) jloop: for j := mc[i-1] + 1; ; j++ { mc[i] = j for k := 0; k <= i; k++ { sum = mc[k] + j if contains(is, sum) { is = is[0:le] continue jloop } is = append(is, sum) } break } } return mc
}
func main() {
mc := mianChowla(100) fmt.Println("The first 30 terms of the Mian-Chowla sequence are:") fmt.Println(mc[0:30]) fmt.Println("\nTerms 91 to 100 of the Mian-Chowla sequence are:") fmt.Println(mc[90:100])
}</lang>
- Output:
The first 30 terms of the Mian-Chowla sequence are: [1 2 4 8 13 21 31 45 66 81 97 123 148 182 204 252 290 361 401 475 565 593 662 775 822 916 970 1016 1159 1312] Terms 91 to 100 of the Mian-Chowla sequence are: [22526 23291 23564 23881 24596 24768 25631 26037 26255 27219]
Perl
<lang perl>use strict; use warnings; use feature 'say';
sub generate_mc {
my($max) = @_; my $index = 0; my $test = 1; my %sums = (2 => 1); my @mc = 1; while ($test++) { my %these = %sums; map { next if ++$these{$_ + $test} > 1 } @mc[0..$index], $test; %sums = %these; $index++; return @mc if (push @mc, $test) > $max-1; }
}
my @mian_chowla = generate_mc(100); say "First 30 terms in the Mian–Chowla sequence:\n", join(' ', @mian_chowla[ 0..29]),
"\nTerms 91 through 100:\n", join(' ', @mian_chowla[90..99]);</lang>
- Output:
First 30 terms in the Mian–Chowla sequence: 1 2 4 8 13 21 31 45 66 81 97 123 148 182 204 252 290 361 401 475 565 593 662 775 822 916 970 1016 1159 1312 Terms 91 through 100: 22526 23291 23564 23881 24596 24768 25631 26037 26255 27219
Perl 6
<lang perl6>my @mian-chowla = 1, |(2..Inf).map: -> $test {
state $index = 1; state %sums = 2 => 1; my $next; my %these = %sums; (|@mian-chowla[^$index], $test).map: { ++$next and last if ++%these{$_ + $test} > 1 }; next if $next; %sums = %these; ++$index; $test
};
put 'First 30 terms in the Mian–Chowla sequence:'; put join ', ', @mian-chowla[^30];
put "\nTerms 91 through 100:"; put join ', ', @mian-chowla[90..99];</lang>
- Output:
First 30 terms in the Mian–Chowla sequence: 1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123, 148, 182, 204, 252, 290, 361, 401, 475, 565, 593, 662, 775, 822, 916, 970, 1016, 1159, 1312 Terms 91 through 100: 22526, 23291, 23564, 23881, 24596, 24768, 25631, 26037, 26255, 27219