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A143538 Triangle read by rows, T(n,k) = 1 if k is prime, 0 otherwise; 1 <= k <= n. 3
0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums = A000720, PrimePi(n), the number of primes through n: (0, 1, 2, 2, 3, 3, 4, 4, 4, 4, ...).

LINKS

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

FORMULA

Triangle read by rows, T(n,k) = 1 if k is prime, 0 otherwise; 1 <= k <= n. A000012 * (A010051 * 0^(n-k)). A010051 * 0^(n-k) = an infinite lower triangular matrix with A010051 (the characteristic function of the primes) as the main diagonal and the rest zeros. The multiplier A000012 takes partial sums of column terms.

EXAMPLE

First few rows of the triangle =

0;

0, 1;

0, 1, 1;

0, 1, 1, 0;

0, 1, 1, 0, 1;

0, 1, 1, 0, 1, 0;

0, 1, 1, 0, 1, 0, 1;

...

MATHEMATICA

Table[If[PrimeQ[k], 1, 0], {n, 1, 20}, {k, 1, n}] // Flatten (* G. C. Greubel, Sep 17 2017 *)

PROG

(PARI) for(n=1, 10, for(k=1, n, print1(if(isprime(k), 1, 0), ", "))) \\ G. C. Greubel, Sep 17 2017

CROSSREFS

Cf. A000720, A010051.

Sequence in context: A092436 A164056 A163539 * A011656 A043545 A094754

Adjacent sequences:  A143535 A143536 A143537 * A143539 A143540 A143541

KEYWORD

nonn,tabl,changed

AUTHOR

Gary W. Adamson, Aug 23 2008

STATUS

approved

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Last modified September 25 18:20 EDT 2017. Contains 292499 sequences.