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A116865
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Characteristic array for partitions with only prime parts.
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3
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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; internal format)
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OFFSET
| 1,1
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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.
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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.
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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.
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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.
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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
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KEYWORD
| nonn,easy,tabf
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 24 2006
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