A141700 Triangle read by rows: A120007 interleaved with (k-1) zeros.

0, 2, 0, 3, 0, 0, 2, 2, 0, 0, 5, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 2, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0

Offset

1,2

Comments

Similar to A140256. At row index equal to a prime power one more prime of that prime power is added each time the prime power increases. At row index equal to lcm of {1,2,3...} the A120007 can be read alliteratively from the right to the left, meaning that A120007 begins over and over again.

This table illustrates the fundamental theorem of arithmetic and the known identity where the row products are the natural numbers A000027. In this formatting the pattern of primes so to say repeats itself endlessly in a layered interleaved manner. The row sums of this table gives A001414.

Links

Table of n, a(n) for n=1..105.

Example

Table begins:
0;
2,0;
3,0,0;
2,2,0,0;
5,0,0,0,0;
0,3,2,0,0,0;
7,0,0,0,0,0,0;

Prog

(Excel) =if(row()>=column(); if(mod(row(); column())=0; lookup(row()/column(); A000027; A120007); 0); "")

Crossrefs

Cf. A120007, A140256, A014963, A001414, A000027.

Sequence in context: A035182 A280720 A245964 * A345228 A357887 A359586

Adjacent sequences: A141697 A141698 A141699 * A141701 A141702 A141703

Keyword

nonn,tabl

Author

Mats Granvik, Jun 30 2008

Status

approved