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A207409 Triangular array: T(n,k) = prime(n) mod prime(k), 1 <= k < n.

%I A207409 #36 Aug 03 2024 13:25:50
%S A207409 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 A207409 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 A207409 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 A207409 Triangular array: T(n,k) = prime(n) mod prime(k), 1 <= k < n.
%C A207409 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 A207409 Robert Israel, <a href="/A207409/b207409.txt">Table of n, a(n) for n = 1..10011</a> (first 141 rows, flattened)
%e A207409 Top 7 rows:
%e A207409   n=2:  1............. 3 mod 2
%e A207409   n=3:  1 2............5 mod 2, 5 mod 3
%e A207409   n=4:  1 1 2..........7 mod 2, 7 mod 3, 7 mod 5
%e A207409   n=5:  1 2 1 4
%e A207409   n=6:  1 1 3 6 2
%e A207409   n=7:  1 2 2 3 6 4
%e A207409   n=8:  1 1 4 5 8 6 2
%p A207409 P := select(isprime, [$1..100]):
%p A207409 seq(seq(P[n] mod P[k],k=1..n-1),n=1..nops(P)); # _Robert Israel_, May 01 2017
%t A207409 t = Table[Mod[Prime[n + 1], Prime[k]], {n, 1, 15}, {k, 1, n }];
%t A207409 Flatten[t]   (* this sequence *)
%t A207409 TableForm[t] (* this sequence as a triangle *)
%o A207409 (PARI) row(n) = my(p=prime(n)); vector(n-1, k, p % prime(k)); \\ _Michel Marcus_, Jul 13 2024
%Y A207409 Cf. A000040.
%Y A207409 Cf. A001223 (right diagonal), A033955 (row sums), A039731 (row maxs).
%K A207409 nonn,tabl
%O A207409 2,3
%A A207409 _Clark Kimberling_, Feb 17 2012