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

1,1

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.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

Nest[Append[#, NextPrime[Total[#]/2]]&, {2}, 100]
nxt[{hs_, a_}]:=With[{sp=NextPrime[hs]}, {hs+sp/2, sp}]; NestList[nxt, {1, 2}, 50][[;; , 2]] (* Harvey P. Dale, Oct 16 2025 *)

Prog

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

Crossrefs

Cf. A070218.

Sequence in context: A077419 A125189 A226498 * A300440 A147997 A218557

Adjacent sequences: A196372 A196373 A196374 * A196376 A196377 A196378

Keyword

nonn

Author

Zak Seidov, Oct 28 2011

Status

approved