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

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, 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, 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

Offset: 2

Author

Clark Kimberling, Feb 17 2012

Keywords

• nonn
• tabl

Comments

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

Examples

			Top 7 rows:
  n=2:  1............. 3 mod 2
  n=3:  1 2............5 mod 2, 5 mod 3
  n=4:  1 1 2..........7 mod 2, 7 mod 3, 7 mod 5
  n=5:  1 2 1 4
  n=6:  1 1 3 6 2
  n=7:  1 2 2 3 6 4
  n=8:  1 1 4 5 8 6 2
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)

Crossrefs

Cf. A000040.

Cf. A001223 (right diagonal), A033955 (row sums), A039731 (row maxs).

Programs

Maple

P := select(isprime, [$1..100]):
seq(seq(P[n] mod P[k],k=1..n-1),n=1..nops(P)); # Robert Israel, May 01 2017

Mathematica

t = Table[Mod[Prime[n + 1], Prime[k]], {n, 1, 15}, {k, 1, n }];
Flatten[t]   (* this sequence *)
TableForm[t] (* this sequence as a triangle *)

PARI

row(n) = my(p=prime(n)); vector(n-1, k, p % prime(k)); \\ Michel Marcus, Jul 13 2024