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

Robert Israel israel at math.ubc.ca
Tue Jun 24 06:03:29 CEST 2008

```
On Mon, 23 Jun 2008, Jonathan Post wrote:

> 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.

Of course you mean noncomposites (i.e. 1 or prime).

The members of the sequence up to 5000 are

2, 3, 5, 7, 11, 13, 47, 61, 73, 107, 167, 179, 313, 347, 421, 479,
719, 863, 1153, 1213, 1283, 1307, 1523, 3467, 3733, 4007, 4621, 4787

if the following Maple program is to be believed.

N:= 5000:
primes,comps:= selectremove(isprime,{\$2..N}):
M:= nops(comps):
X:= primes:
for n from 1 to floor(sqrt(2*N)) do
i:= 1;
T:= add(comps[k],k=1..n);
while T <= N do
X := X minus {T};
if i + n > M then break fi;
T := T + comps[i+n] - comps[i];
i := i+1;
od;
od:
X;

Cheers,
Robert

At 9:06 PM -0700 6/23/08, Robert Israel wrote:
>On Mon, 23 Jun 2008, Jonathan Post wrote:
>
>> 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.
>
>Of course you mean noncomposites (i.e. 1 or prime).
>
>The members of the sequence up to 5000 are
>
>2, 3, 5, 7, 11, 13, 47, 61, 73, 107, 167, 179, 313, 347, 421, 479,
>719, 863, 1153, 1213, 1283, 1307, 1523, 3467, 3733, 4007, 4621, 4787

Correction. A037174 does not use 1.  With 1 and the composites, the

Looks like A037174 (Primes which are not the sum of consecutive composite
numbers).

Tony

At 9:06 PM -0700 6/23/08, Robert Israel wrote:
>On Mon, 23 Jun 2008, Jonathan Post wrote:
>
>> 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.
>
>Of course you mean noncomposites (i.e. 1 or prime).
>
>The members of the sequence up to 5000 are
>
>2, 3, 5, 7, 11, 13, 47, 61, 73, 107, 167, 179, 313, 347, 421, 479,
>719, 863, 1153, 1213, 1283, 1307, 1523, 3467, 3733, 4007, 4621, 4787

Looks like A037174 (where 1 is taken as composite).

Tony

```

More information about the SeqFan mailing list