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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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified December 15 17:45 EST 2018. Contains 318150 sequences. (Running on oeis4.)