OFFSET
1,1
COMMENTS
This algorithm acts as a prime number sieve. Prime numbers move to the left with each step. The second diagonal (and all the numbers to the left) are all primes.
The first composite number in each row: 4, 8, 8, 16, 16, 24, 24, 32, 32, 32, 45, 48, 48, 54, 64, 64, 64, 72, 80, 81, 90, 96, 105, 108, 108, 120, 128, 128, 128, ....
In this sieve, some numbers disappear and then reappear. For example, 26 disappears on the third row, then reappears on the 4th and 5th rows, then disappears again.
EXAMPLE
Table begins:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...
2, 3, 5, 7, 8, 9, 11, 13, 14, 15, 17, 19, 20, 21, 23, 25, ...
2, 3, 5, 7, 8, 9, 11, 13, 14, 15, 17, 19, 22, 23, 25, 27, ...
2, 3, 5, 7, 11, 13, 16, 17, 19, 21, 23, 25, 26, 29, 31, 33, ...
2, 3, 5, 7, 11, 13, 16, 17, 19, 21, 23, 25, 26, 29, 31, 33, ...
2, 3, 5, 7, 11, 13, 17, 19, 23, 24, 25, 29, 31, 37, 41, 43, ...
2, 3, 5, 7, 11, 13, 17, 19, 23, 24, 25, 29, 31, 37, 41, 43, ...
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 32, 35, 37, 39, 41, ...
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 32, 37, 41, 43, 45, ...
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 32, 37, 41, 43, 45, ...
E.g., in the third row, a(3,1)=2, and every 4 consecutive terms are pairwise coprime.
PROG
(PARI) row(N, howmany=100)=my(v=List(primes(N))); for(i=N+1, howmany, my(L=lcm(v[#v-N+1..#v]), n=v[#v]); while(gcd(n, L)>1, n++); listput(v, n)); Vec(v) \\ Charles R Greathouse IV, Oct 27 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ali Sada, Oct 26 2019
STATUS
approved