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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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified March 3 12:16 EST 2021. Contains 341762 sequences. (Running on oeis4.)