# Seq: Natural numbers that cannot be written as a sum of one or more consecutive composites

Jonathan Post jvospost3 at gmail.com
Tue Jun 24 03:07:26 CEST 2008

```1, 2, 3, 5, 7, 11, 13, 47, 61, 73, [no more through 101]

Natural numbers that cannot be written as a sum of one or more
consecutive composites (A002808).

These must be nonprimes. This is the complement of [A002808 UNION
A053767 UNION {sum of consecutive composites starting with 6} UNION
{sum of consecutive composites starting with 8} UNION {sum of
consecutive composites starting with 9} UNION {sum of consecutive
composites starting with 10} UNION ...]

The primes not in the sequence begin:
17 = 8+9
19 = 9+10
23 = 6+8+9
29 = 14+15
31 = 9+10+12
37 = 4+6+8+9+10
41 = 12+14+15
43 = 21+22
53 = 8+9+10+12+14 = 26+27
59 = 6+8+9+10+12+14 = 15+16+18
67 = 10+12+14+15+16 = 33+34
71 = 35+36
79 = 15+16+18+20 = 39+40
83 = 14+15+16+18+20
89 = 44+45
97 = 16+18+20+21+22 = 48+49
101 = 50+51

etc.

Cf. A002808, A053767, A055514

Is this interesting to anyone?

Is the sequence finite or infinite? What is its density?

-- Jonathan Vos Post

```