

A147693


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


3



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
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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(n1)+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: A089310 A129753 A307247 * A070936 A014081 A091890
Adjacent sequences: A147690 A147691 A147692 * A147694 A147695 A147696


KEYWORD

easy,nonn,tabf


AUTHOR

Reikku Kulon, Nov 10 2008


STATUS

approved



