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

1,2

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).

Links

Table of n, a(n) for n=1..49.

Example

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.

Sequence in context: A283668 A191581 A192896 * A228206 A195734 A018177

Adjacent sequences: A115027 A115028 A115029 * A115031 A115032 A115033

Keyword

nonn

Author

Reinhard Zumkeller, Feb 25 2006

Status

approved