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 A050936 Sum of two or more consecutive prime numbers. 27
 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; text; internal format)
 OFFSET 1,1 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Patrick De Geest, WONplate 122 Carlos Rivera, Puzzle 46. Primes expressible as sum of consecutive primes in K ways, The Prime Puzzles and Problems Connection. Eric Weisstein's World of Mathematics, Prime Sums 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. MAPLE # uses code of A084143 isA050936 := proc(n::integer) if A084143(n) >= 1 then true; else false; end if; end proc: for n from 1 to 300 do if isA050936(n) then printf("%d, ", n); end if; end do: # R. J. Mathar, Aug 19 2020 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] (* Vladimir Joseph Stephan 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 &] (* Robert G. Wilson v *) Module[{nn=70, prs}, prs=Prime[Range[nn]]; Take[Union[Flatten[Table[Total/@ Partition[prs, i, 1], {i, 2, nn}]]], nn]] (* Harvey P. Dale, Nov 13 2013 *) 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 (PARI) is(n)=my(v, m=1, t); while(1, v=vector(m++); v[m\2]=precprime(n\m); for(i=m\2+1, m, v[i]=nextprime(v[i-1]+1)); forstep(i=m\2-1, 1, -1, v[i]=precprime(v[i+1]-1)); if(v[1]==0, return(0)); t=vecsum(v); if(t==n, return(1)); if(t>n, while(t>n, t-=v[m]; v=concat(precprime(v[1]-1), v[1..m-1]); t+=v[1]), while(tlim, return(Set(v))); listput(v, s); forprime(q=prime(n+1), , s+=q-p; if(s>lim, break); listput(v, s); p=nextprime(p+1))); \\ Charles R Greathouse IV, Nov 24 2021 CROSSREFS Subsequence of A034707. Cf. A067372 up to A067381, A054996, A000040. A084143(a(n)) > 0, complement of A087072. Cf. A054845, A097889. Sequence in context: A314379 A153663 A065528 * A084146 A314380 A332513 Adjacent sequences: A050933 A050934 A050935 * A050937 A050938 A050939 KEYWORD nice,nonn,easy AUTHOR G. L. Honaker, Jr., Dec 31 1999 EXTENSIONS More terms from David W. Wilson, Jan 13 2000 STATUS approved

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Last modified November 28 10:39 EST 2022. Contains 358411 sequences. (Running on oeis4.)