A351124 a(n) is the least k > 0 such that the set { prime(n), ..., prime(n+k-1) } can be partitioned into two disjoint sets with equal sum, or -1 if no such k exists (prime(n) denotes the n-th prime number).

3, 6, 4, 4, 4, 4, 8, 10, 4, 8, 8, 4, 10, 14, 6, 4, 6, 6, 8, 8, 4, 8, 12, 10, 4, 4, 4, 8, 4, 8, 6, 10, 4, 6, 8, 18, 4, 6, 8, 6, 4, 12, 4, 8, 10, 6, 10, 4, 8, 6, 8, 12, 10, 4, 6, 4, 8, 8, 10, 8, 12, 8, 4, 12, 6, 6, 8, 8, 14, 8, 4, 8, 10, 4, 10, 6, 4, 10, 8, 4, 4

Offset

1,1

Comments

Conjecture: all terms are positive.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Formula

a(n) = 4 iff n belongs to A022884.

Example

The first terms, alongside an appropriate partition {P, Q}, are:
  n   a(n)  P                     Q
  --  ----  --------------------  --------------------
   1     3  {2, 3}                {5}
   2     6  {3, 5, 7, 13}         {11, 17}
   3     4  {5, 13}               {7, 11}
   4     4  {7, 17}               {11, 13}
   5     4  {11, 19}              {13, 17}
   6     4  {13, 23}              {17, 19}
   7     8  {17, 29, 31, 43}      {19, 23, 37, 41}
   8    10  {19, 31, 41, 47, 53}  {23, 29, 37, 43, 59}
   9     4  {23, 37}              {29, 31}
  10     8  {29, 41, 47, 53}      {31, 37, 43, 59}

Prog

(PARI) a(n) = { my (s=[0], k=0); forprime (p=prime(n), oo, s=setunion(apply (v -> v-p, s), apply (v -> v+p, s)); k++; if (setsearch(s, 0), return (k))) }

Crossrefs

Cf. A022884.

Sequence in context: A308291 A006464 A233825 * A159354 A196500 A023676

Adjacent sequences: A351121 A351122 A351123 * A351125 A351126 A351127

Keyword

nonn

Author

Rémy Sigrist, Feb 02 2022

Status

approved