A067773 a(n) is the unique positive integer m which has a self-conjugate partition whose parts are the first n primes.

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

Offset: 1

Author

Naohiro Nomoto, Feb 06 2002

Keywords

• easy
• nonn

Comments

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

Examples

			2+2 = 4; 2+3+3 = 8; 2+2+3+5+5 = 17; ....
		

Crossrefs

Cf. A000700, A014342.

Programs

Mathematica

a[n_] := 2Prime[n]+Sum[Prime[n-i](Prime[i+1]-Prime[i]), {i, 1, n-1}]

Formula

a(n) = 2 prime(n) + Sum_{i=1..n-1} prime(n-i)*(prime(i+1)-prime(i)) = A014342(n-1) - A014342(n-2).

Extensions

Edited by Dean Hickerson, Feb 12 2002

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