1,9

Given M = the infinite lower triangular matrix A130460, and V = any nonzero sequence with initial term "k", M*V = [k,...(1, 2, 3,...) dot (V)]. Example: say V = the sequence of primes as a Vector: [2, 3, 5, 7...]. Then M*V = [2, 2, 6, 15, 28, 55, 78,...]; since k = 2, and (1, 2, 3,...) dot (2, 3, 5, 7,...) = 2, 6, 15, 28, 55,...]. Given V = [1, 2, 3,...], then M*V = [1, 1, 4, 9, 16, 25, 36,...]. Repeated iterates of M*V = ANS, then M*ANS, etc..., quickly generates a sequence tending to k * [1, 1, 2, 6, 24, 120,...]. Since k = 2 in [2, 3, 5, 7,...] repeated iterates of the operation tends to [2, 2, 4, 12, 48, 240,...] = 2 * [1, 1, 2, 6, 24, 120,...].

A natural number operator as an infinite lower triangular matrix M. (1,0,0,0,...) in the main diagonal, (1,2,3,...) in the subdiagonal, and the rest zeros.

First few rows of the triangle are:

1;

1, 0;

0, 2, 0;

0, 0, 3, 0;

0, 0, 0, 4, 0;

0, 0, 0, 0, 5, 0;

...

Cf. A130461, A130476, A130477, A130478.

Sequence in context: A111417 A007271 A035656 this_sequence A097017 A108707 A046775

Adjacent sequences: A130457 A130458 A130459 this_sequence A130461 A130462 A130463

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), May 28 2007