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A196375
a(1)=2; a(n)=smallest prime greater than the half-sum of all previous terms.
1
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.
MATHEMATICA
Nest[Append[#, NextPrime[Total[#]/2]]&, {2}, 100]
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
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 28 2011
STATUS
approved