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A115030 Number of distinct sums of subsets of the first n prime numbers. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 9 15:21 EDT 2021. Contains 343742 sequences. (Running on oeis4.)