A116865 Characteristic array for partitions with only prime parts.

0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0

Offset: 1

Author

Wolfdieter Lang, Mar 24 2006

Keywords

• nonn
• easy
• tabf

Comments

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.

Examples

			[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.
		

Links

• 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.

Crossrefs

See also array A116864.

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

Formula

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.