A196375 a(1)=2; a(n)=smallest prime greater than the half-sum of all previous terms.

2, 2, 3, 5, 7, 11, 17, 29, 41, 59, 89, 137, 211, 307, 461, 691, 1039, 1559, 2339, 3511, 5261, 7901, 11863, 17783, 26669, 40009, 60013, 90011, 135017, 202529, 303803, 455701, 683567, 1025327, 1537997, 2307031, 3460517, 5190769, 7786151, 11679223, 17518843, 26278261

Offset: 1

Author

Zak Seidov, Oct 28 2011

Keywords

• nonn

Comments

a(n) <= A070218(n).

If we introduce k in the name "(sum of all previous terms)/k", then cases k=1,2 correspond to A070218, A196375, and in general case, the sequence begins with k 2's, with gradually (not monotonically) decreasing multiplicity of terms; e.g., at case k=10 the sequence begins: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 11, 11, 11, 11, 13, 17, 17, 17, 19, 23, 23, 29, 29, 31, 37, 41.

Crossrefs

Cf. A070218.

Programs

Mathematica

Nest[Append[#,NextPrime[Total[#]/2]]&,{2},100]

PARI

print1(s=2);for(i=2,99,print1(", ",t=nextprime(s/2));s+=t) \\ Charles R Greathouse IV, Dec 31 2011