

A116865


Characteristic array for partitions with only prime parts.


3



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
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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 AbramowitzStegun (ASt), pp. 8312.


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 kth partition of n, in the AbramowitzStegun 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 ASt 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: A156259 A138710 A179829 * A157687 A127266 A083923
Adjacent sequences: A116862 A116863 A116864 * A116866 A116867 A116868


KEYWORD

nonn,easy,tabf


AUTHOR

Wolfdieter Lang, Mar 24 2006


STATUS

approved



