A115030 Number of distinct sums of subsets of the first n prime numbers.

1, 3, 6, 11, 22, 35, 52, 71, 94, 123, 154, 191, 232, 275, 322, 375, 434, 495, 562, 633, 706, 785, 868, 957, 1054, 1155, 1258, 1365, 1474, 1587, 1714, 1845, 1982, 2121, 2270, 2421, 2578, 2741, 2908, 3081, 3260, 3441, 3632, 3825, 4022, 4221, 4432, 4655, 4882

Offset: 1

Author

Reinhard Zumkeller, Feb 25 2006

Keywords

• nonn

Comments

a(n) = A007504(n) - 6 for n>3, the 6 numbers that can't be written as sum of distinct primes not greater A000040(n) are {1,4,6,s-6,s-4,s-1} with s=A007504(n).

Examples

			n=4 (2, 3, 5 and 7): 2, 3, 5=2+3, 7=2+5, 8=3+5, 9=2+7,
10=2+3+5=3+7,
12=2+3+7=5+7, 14=2+5+7, 15=3+5+7 and 17=2+3+5+7:
a(4) = {2, 3, 5, 7, 8, 9, 10, 12, 14, 15, 17} = 11.
		

Crossrefs

Cf. A000586.