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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: A164056 A286059 A163539 * A242018 A288132 A324903

Adjacent sequences:  A143535 A143536 A143537 * A143539 A143540 A143541

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Aug 23 2008

STATUS

approved

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Last modified May 18 16:07 EDT 2021. Contains 343995 sequences. (Running on oeis4.)