A147693 Triangle read by rows: numbers n and prime numbered columns p such that T(n, p) is n mod p.

0, 1, 0, 0, 1, 1, 2, 0, 0, 0, 1, 1, 1, 2, 0, 0, 2, 3, 1, 1, 0, 4, 2, 0, 1, 0, 3, 1, 2, 1, 4, 0, 0, 0, 2, 5, 1, 1, 1, 3, 6, 2, 0, 0, 2, 4, 0, 3, 1, 1, 0, 0, 1, 4, 2, 0, 1, 1, 2, 5, 3, 1, 2, 2, 3, 6, 4, 0, 0, 0, 3, 4, 7, 5, 1, 1, 1, 4, 5, 8, 6, 2, 0, 0, 2, 0, 6, 9, 7, 3, 1, 1, 0, 1, 0, 10, 8, 4, 2

Offset

2,7

Comments

The triangle begins with T(2, 2).

A number p is prime, beginning a new column, iff T(p, k) is nonzero for all k < p; T(p, p) is then 0.

Each row can be produced from the previous row by adding one to each number and resetting to zero any which would equal their column number. A complex pattern emerges if values in the triangle are taken modulo 2.

Rows are unique. Row n has length A000720(n). - Jason Kimberley, Nov 2012

Links

Jason Kimberley, Rows n = 2..294 of irregular triangle, flattened

Eric Weisstein's World of Mathematics, Redheffer Matrix

Formula

a(A046992(n-1)+i) = T(n,i) = n mod A000040(i), where 1 <= i <= A000720(n). Jason Kimberley, Nov 21 2012

Example

The triangle begins as so:
[2] 0
[3] 1 0
... 0 1
[5] 1 2 0
... 0 0 1
[7] 1 1 2 0
... 0 2 3 1
... 1 0 4 2
... 0 1 0 3

Prog

(Magma) A147693 :=
func< n | [n mod p:p in PrimesUpTo(n)] >;
[A147693(n):n in[2..19]]; // Jason Kimberley, Nov 28 2012

Crossrefs

Cf. A002321, A083058.

Sequence in context: A129753 A356324 A307247 * A070936 A014081 A091890

Adjacent sequences: A147690 A147691 A147692 * A147694 A147695 A147696

Keyword

easy,nonn,tabf

Author

Reikku Kulon, Nov 10 2008

Status

approved