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A050936
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Sum of two or more consecutive prime numbers.
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27
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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;
text;
internal format)
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OFFSET
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1,1
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LINKS
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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
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EXAMPLE
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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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MAPLE
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# 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
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MATHEMATICA
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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 *)
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PROG
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(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(t<n, t-=v[1]; v=concat(v[2..m], nextprime(v[m]+1)); t+=v[m])); if(v[1]==0, return(0)); if(t==n, return(1))) \\ Charles R Greathouse IV, May 05 2016
(PARI) list(lim)=my(v=List(), s, n=1, p); while(1, p=2; s=vecsum(primes(n++)); if(s>lim, 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
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CROSSREFS
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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
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KEYWORD
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nice,nonn,easy
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AUTHOR
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G. L. Honaker, Jr., Dec 31 1999
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EXTENSIONS
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More terms from David W. Wilson, Jan 13 2000
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STATUS
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approved
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