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A066028 Largest prime which can be written as a sum of distinct primes <= prime(n).

%I A066028 #17 Aug 05 2016 14:01:38
%S A066028 2,5,7,17,23,41,53,67,97,127,157,197,233,281,317,379,433,499,563,631,
%T A066028 709,773,863,953,1051,1153,1259,1361,1471,1583,1709,1831,1979,2113,
%U A066028 2273,2417,2579,2731,2909,3079,3259,3433,3631,3823,4021,4219,4423,4651
%N A066028 Largest prime which can be written as a sum of distinct primes <= prime(n).
%C A066028 Sequence is nondecreasing by definition. Is it strictly increasing? - _Charles R Greathouse IV_, Jun 20 2013
%C A066028 a(n) = A256015(n,A108018(n)). - _Reinhard Zumkeller_, Jun 01 2015
%H A066028 T. D. Noe, <a href="/A066028/b066028.txt">Table of n, a(n) for n = 1..1000</a>
%e A066028 n = 5: the following primes are sums of primes <= 11 = A000040(5): 2, 3, 5, 7, 11, 13, 17, 19 and 23 = 5+7+11 = 2+3+7+11, so a(5) = 23.
%t A066028 Reap[Do[a = {1, 4, 6}; s = Sum[Prime[i], {i, 1, n}]; q = s; While[ !PrimeQ[q] || Length[ Position[a, s - q]] > 0, q = NextPrime[q, -1]]; Print[q]; Sow[q], {n, 1, 60}]][[2, 1]] (* updated by _Jean-François Alcover_, Feb 10 2015 *)
%t A066028 Table[Max[Select[Total/@Subsets[Prime[Range[n]],{Max[1,n-5],n}],PrimeQ]],{n,50}] (* To shorten computation time, the program only tests for the subsets of primes equal to n, n-1, n-2, n-3, n-4, and n-5 in length. *) (* _Harvey P. Dale_, Aug 05 2016 *)
%o A066028 (Haskell)
%o A066028 import Data.List (subsequences)
%o A066028 a066028 = maximum . filter ((== 1) . a010051') .
%o A066028                     map sum . tail . subsequences . flip take a000040_list
%o A066028 -- _Reinhard Zumkeller_, Jun 01 2015
%Y A066028 Cf. A007504.
%Y A066028 Cf. A010051, A000040, A108018, A256015.
%K A066028 nice,nonn
%O A066028 1,1
%A A066028 _Reinhard Zumkeller_, Dec 11 2001
%E A066028 More terms from _Robert G. Wilson v_, Dec 12 2001