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

2, 5, 7, 17, 23, 41, 53, 67, 97, 127, 157, 197, 233, 281, 317, 379, 433, 499, 563, 631, 709, 773, 863, 953, 1051, 1153, 1259, 1361, 1471, 1583, 1709, 1831, 1979, 2113, 2273, 2417, 2579, 2731, 2909, 3079, 3259, 3433, 3631, 3823, 4021, 4219, 4423, 4651

Offset: 1

Author

Reinhard Zumkeller, Dec 11 2001

Keywords

• nice
• nonn

Comments

Sequence is nondecreasing by definition. Is it strictly increasing? - Charles R Greathouse IV, Jun 20 2013

a(n) = A256015(n,A108018(n)). - Reinhard Zumkeller, Jun 01 2015

Examples

			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.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007504.

Cf. A010051, A000040, A108018, A256015.

Programs

Haskell

import Data.List (subsequences)
a066028 = maximum . filter ((== 1) . a010051') .
                    map sum . tail . subsequences . flip take a000040_list
-- Reinhard Zumkeller, Jun 01 2015

Mathematica

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 *)
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 *)

Extensions

More terms from Robert G. Wilson v, Dec 12 2001