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

1,1

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.

Links

Table of n, a(n) for n=1..81.

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.

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.

Example

[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.

Crossrefs

See also array A116864.

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

Sequence in context: A172486 A288223 A353811 * A353674 A288512 A157687

Adjacent sequences: A116862 A116863 A116864 * A116866 A116867 A116868

Keyword

nonn,easy,tabf

Author

Wolfdieter Lang, Mar 24 2006

Status

approved