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

[Robert Israel]

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