1,1

The row length sequence of this array is p(n)=A000041(n) (number of partitions).

The partitions of n are ordered according to Abramowitz-Stegun (A-St), pp. 831-2.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972.

W. Lang: First 10 rows.

a(n,k)= 1 if the k-th partition of n, in the Abramowitz-Stegun order, has only prime parts, else 0. See A000040 for the prime numbers.

[0];[1, 0]; [1, 0, 0]; [0, 0, 1, 0, 0]; [1, 0, 1, 0, 0, 0, 0]; ...

a(4,3)=1 because the third partition of 4 is, in A-St order, (2,2)

which has only prime numbers as parts. Each of the other four partitions of 4

has at least one part which is not a prime number.

See also array A116864.

Row sums give A000607(n), n>=1.

Sequence in context: A156259 A038219 A138710 this_sequence A157687 A127266 A083923

Adjacent sequences: A116862 A116863 A116864 this_sequence A116866 A116867 A116868

nonn,easy,tabf

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 24 2006