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A050936
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Sum of two or more consecutive prime numbers.
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16
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5, 8, 10, 12, 15, 17, 18, 23, 24, 26, 28, 30, 31, 36, 39, 41, 42, 48, 49, 52, 53, 56, 58, 59, 60, 67, 68, 71, 72, 75, 77, 78, 83, 84, 88, 90, 95, 97, 98, 100, 101, 102, 109, 112, 119, 120, 121, 124, 127, 128, 129, 131, 132, 138, 139, 143, 144, 150, 152, 155, 156, 158, 159, 160, 161, 162
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
P. De Geest, WONplate 122
C. Rivera, Puzzle 46
Eric Weisstein's World of Mathematics, Prime Sums
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EXAMPLE
| E.g. 5 = (2 + 3) or (#2,2).
2+3 = 5, 3+5 = 8, 2+3+5 = 10, 7+5 = 12, 3+5+7 = 15, etc.
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MATHEMATICA
| lst={}; Do[p=Prime[n]; Do[p=p+Prime[k]; AppendTo[lst, p], {k, n+1, 2*10^2}], {n, 2*10^2}]; Take[Union[lst], 10^2] [From Vladimir Orlovsky , Aug 21 2008]
f[n_] := Block[{len = PrimePi@ n}, p = Prime@ Range@ len; Count[ Flatten[ Table[ p[[i ;; j]], {i, len}, {j, i+1, len}], 1], q_ /; Total@ q == n]]; Select[ Range@ 150, f@ # > 0 &] (* Or quicker for a larger range *)
lmt = 150; p = Prime@ Range@ PrimePi@ lmt; t = Table[0, {lmt}]; Do[s = 0; j = i+1; While[s = s + p[[j]]; s <= lmt, t[[s]]++; j++], {i, Length@ p}]; Select[ Range@ lmt, t[[#]] > 0 &] (* RGWv *)
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PROG
| (Haskell)
import Data.Set (empty, findMin, deleteMin, insert)
import qualified Data.Set as Set (null)
a050936 n = a050936_list !! (n-1)
a050936_list = f empty [2] 2 $ tail a000040_list where
f s bs c (p:ps)
| Set.null s || head bs <= m = f (foldl (flip insert) s bs') bs' p ps
| otherwise = m : f (deleteMin s) bs c (p:ps)
where m = findMin s
bs' = map (+ p) (c : bs)
-- Reinhard Zumkeller, Aug 26 2011
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CROSSREFS
| Cf. A067372 up to A067381, A054996, A000040.
A084143(a(n)) > 0, complement of A087072.
Cf. A034707, A054845, A097889.
Sequence in context: A115401 A153663 A065528 * A084146 A087280 A022413
Adjacent sequences: A050933 A050934 A050935 * A050937 A050938 A050939
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KEYWORD
| nice,nonn,easy
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AUTHOR
| G. L. Honaker, Jr. (honak3r(AT)gmail.com), Dec 31 1999
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net), Jan 13, 2000.
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