A256015 -id:A256015 - cp's OEIS frontend

A108018 a(n) = the number of primes representable as the sum of some subset of the set of first n primes.

1, 3, 4, 5, 9, 12, 16, 19, 25, 31, 37, 43, 51, 59, 66, 75, 84, 95, 103, 115, 127, 137, 150, 162, 177, 191, 205, 218, 233, 250, 267, 282, 299, 319, 338, 359, 376, 399, 421, 440, 461, 481, 508, 531, 556, 578, 602, 629, 653, 683, 707, 737, 765, 793, 824, 853, 883

Offset: 1

Max Alekseyev, Sep 08 2006

nonn

a(n) = length of n-th row in A256015; A066028(n) = A256015(n,a(n)). - Reinhard Zumkeller, Jun 01 2015

Alois P. Heinz, Table of n, a(n) for n = 1..500

Cf. A071810 (same count but with multiplicities).
Cf. A010051, A000040.
Cf. A066028, A256015.

import Data.List (subsequences, nub)
a108018 = sum . map a010051' . nub . map sum .
          tail . subsequences . flip take a000040_list
-- Reinhard Zumkeller, Dec 16 2013

(* This program is not suitable to compute a large number of terms. *)
a[n_] := a[n] = Select[Total /@ Subsets[Table[Prime[i], {i, 1, n}]], PrimeQ] // Union // Length;
Table[Print[n, " ", a[n]]; a[n], {n, 1, 25}] (* Jean-François Alcover, Mar 12 2019 *)

More terms from Alois P. Heinz, Oct 24 2015

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

Original entry on oeis.org

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

Reinhard Zumkeller, Dec 11 2001

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

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

Cf. A007504.

Cf. A010051, A000040, A108018, A256015.

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

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 *)

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

cp's OEIS Frontend

A108018 a(n) = the number of primes representable as the sum of some subset of the set of first n primes.

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