A074589 - OEIS

A074589

Replace each number n in Pascal's triangle with the n-th prime.

2, 2, 2, 2, 3, 2, 2, 5, 5, 2, 2, 7, 13, 7, 2, 2, 11, 29, 29, 11, 2, 2, 13, 47, 71, 47, 13, 2, 2, 17, 73, 149, 149, 73, 17, 2, 2, 19, 107, 263, 349, 263, 107, 19, 2, 2, 23, 151, 433, 701, 701, 433, 151, 23, 2, 2, 29, 197, 659, 1291, 1601, 1291, 659, 197, 29, 2

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

OFFSET

0,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..999

FORMULA

T(n,k) = A000040(A007318(n,k)).

EXAMPLE

Triangle begins:

2, 2;

2, 3, 2;

2, 5, 5, 2;

2, 7, 13, 7, 2;

2, 11, 29, 29, 11, 2;

2, 13, 47, 71, 47, 13, 2;

2, 17, 73, 149, 149, 73, 17, 2;

...

MAPLE

T:= (n, k)-> ithprime(binomial(n, k)):

seq(seq(T(n, k), k=0..n), n=0..10); # Alois P. Heinz, Feb 22 2026

MATHEMATICA

Prime[#]&/@(Table[Binomial[n, k], {n, 0, 10}, {k, 0, n}]//Flatten) (* Harvey P. Dale, Apr 09 2017 *)

PROG

(PARI) lista(nn) = {for (n=0, nn, for (k=0, n, print1(prime(binomial(n, k)), ", "); ); ); } \\ Michel Marcus, May 18 2013

CROSSREFS

Cf. A000040, A007318, A074663 (row sums).

Sequence in context: A324818 A233417 A299741 * A199800 A338094 A165035

Adjacent sequences: A074586 A074587 A074588 * A074590 A074591 A074592

KEYWORD

easy,nonn,tabl

AUTHOR

Joseph L. Pe, Sep 26 2002

EXTENSIONS

More terms from Michel Marcus, May 18 2013

Offset changed for consistency with A007318 by Sean A. Irvine, Jan 22 2025

STATUS

approved