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Search: id:A067773
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| A067773 |
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a(n) is the unique positive integer m which has a self-conjugate partition whose parts are the first n primes. |
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+0
1
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| 4, 8, 17, 29, 53, 77, 117, 157, 217, 289, 369, 469, 585, 713, 849, 1025, 1197, 1393, 1617, 1845, 2113, 2373, 2661, 2973, 3321, 3681, 4045, 4481, 4865, 5285, 5793, 6253, 6785, 7341, 7949, 8513, 9169, 9765, 10473, 11233, 11969, 12733, 13541, 14337
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In general, given a finite set of positive integers p(1) < ... < p(n), there's a unique self-conjugate partition using these parts; p(n) occurs p(1) times and p(n-i) occurs p(i+1)-p(i) times for 1<=i<n.
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FORMULA
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a(n) = 2 prime(n) + sum from i=1 to n-1 of prime(n-i)*(prime(i+1)-prime(i)) = A014342(n-1)-A014342(n-2).
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EXAMPLE
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2+2=4; 2+3+3=8; 2+2+3+5+5=17;....
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MATHEMATICA
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a[n_] := 2Prime[n]+Sum[Prime[n-i](Prime[i+1]-Prime[i]), {i, 1, n-1}]
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CROSSREFS
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Cf. A000700, A014342.
Sequence in context: A026393 A092321 A026353 this_sequence A008372 A005697 A115618
Adjacent sequences: A067770 A067771 A067772 this_sequence A067774 A067775 A067776
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KEYWORD
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easy,nonn
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AUTHOR
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Naohiro Nomoto (n_nomoto(AT)yabumi.com), Feb 06 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Feb 12 2002
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