A141700 - OEIS

%I #3 Jul 03 2016 00:15:24

%S 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,

%T 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,

%U 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

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

%C 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.

%C 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.

%e Table begins:

%e 0;

%e 2,0;

%e 3,0,0;

%e 2,2,0,0;

%e 5,0,0,0,0;

%e 0,3,2,0,0,0;

%e 7,0,0,0,0,0,0;

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

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

%K nonn,tabl

%O 1,2

%A _Mats Granvik_, Jun 30 2008