A242261 Lexicographically last sequence such that every odd prime is the sum of at least two terms of the sequence.

1, 2, 4, 10, 18, 36, 72, 148, 156, 312, 456, 1068, 2136, 2436, 6552, 12036, 17976, 29400, 46308, 93228, 119736, 200928, 509556, 911412, 1351812, 2665080, 3978348, 7988688, 17315172, 18646416

Offset

1,2

Comments

Every term is 1 less than a prime.

Links

Table of n, a(n) for n=1..30.

Example

3 could be represented by 1+2 or 0+3, but 1,2 is lexicographically later than 0,3; so the sequence starts with 1,2.
Once 4 is added to sequence for 1+4 = 5, 7 = 1+2+4 is already a sum. So the next thing we need to add is 10 for 1+10=11.

Prog

(PARI) issum(v, k, tot, n)={if(n>=tot, n==tot,
   n==0||(n>=v[k]&&issum(v, k-1, tot-v[k], n-v[k]))||issum(v, k-1, tot-v[k], n))}
al(n) = {local(r=vector(n), k=1, p=3, tot=1); r[1]=1;
   while(k<n, if(!issum(r, k, tot, p), tot+=r[k++]=p-1); p=nextprime(p+1));
   r}

Crossrefs

Sequence in context: A320098 A320968 A279359 * A189892 A240877 A218008

Adjacent sequences: A242258 A242259 A242260 * A242262 A242263 A242264

Keyword

nonn

Author

Franklin T. Adams-Watters, May 09 2014

Status

approved