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A328739 Table of A(n,k) read by antidiagonals, where A(n,1)=2, and every n+1 consecutive terms in row n are pairwise coprime. Terms are chosen to be the least increasing value compatible with these constraints. 1
2, 3, 2, 4, 3, 2, 5, 5, 3, 2, 6, 7, 5, 3, 2, 7, 8, 7, 5, 3, 2, 8, 9, 8, 7, 5, 3, 2, 9, 11, 9, 11, 7, 5, 3, 2, 10, 13, 11, 13, 11, 7, 5, 3, 2, 11, 14, 13, 16, 13, 11, 7, 5, 3, 2, 12, 15, 14, 17, 16, 13, 11, 7, 5, 3, 2, 13, 17, 15, 19, 17, 17, 13, 11 (list; table; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Sequence in context: A089215 A238766 A325239 * A304088 A286597 A358667
KEYWORD
nonn,tabl
AUTHOR
Ali Sada, Oct 26 2019
STATUS
approved

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Last modified July 18 06:54 EDT 2024. Contains 374377 sequences. (Running on oeis4.)