%I #36 Aug 03 2024 13:25:50
%S 1,1,2,1,1,2,1,2,1,4,1,1,3,6,2,1,2,2,3,6,4,1,1,4,5,8,6,2,1,2,3,2,1,10,
%T 6,4,1,2,4,1,7,3,12,10,6,1,1,1,3,9,5,14,12,8,2,1,1,2,2,4,11,3,18,14,8,
%U 6,1,2,1,6,8,2,7,3,18,12,10,4,1,1,3,1,10,4,9,5,20,14,12,6,2,1
%N Triangular array: T(n,k) = prime(n) mod prime(k), 1 <= k < n.
%C Conjecture: For each row in the triangle, the maximum value occurs only once, and for n>2 it is never the first entry and the value previous to it in the row is always odd. - _Mike Jones_, Jul 12 2024
%H Robert Israel, <a href="/A207409/b207409.txt">Table of n, a(n) for n = 1..10011</a> (first 141 rows, flattened)
%e Top 7 rows:
%e n=2: 1............. 3 mod 2
%e n=3: 1 2............5 mod 2, 5 mod 3
%e n=4: 1 1 2..........7 mod 2, 7 mod 3, 7 mod 5
%e n=5: 1 2 1 4
%e n=6: 1 1 3 6 2
%e n=7: 1 2 2 3 6 4
%e n=8: 1 1 4 5 8 6 2
%p P := select(isprime, [$1..100]):
%p seq(seq(P[n] mod P[k],k=1..n-1),n=1..nops(P)); # _Robert Israel_, May 01 2017
%t t = Table[Mod[Prime[n + 1], Prime[k]], {n, 1, 15}, {k, 1, n }];
%t Flatten[t] (* this sequence *)
%t TableForm[t] (* this sequence as a triangle *)
%o (PARI) row(n) = my(p=prime(n)); vector(n-1, k, p % prime(k)); \\ _Michel Marcus_, Jul 13 2024
%Y Cf. A000040.
%Y Cf. A001223 (right diagonal), A033955 (row sums), A039731 (row maxs).
%K nonn,tabl
%O 2,3
%A _Clark Kimberling_, Feb 17 2012