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A050936
Sum of two or more consecutive prime numbers.
28
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
OFFSET
1,1
LINKS
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(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
CROSSREFS
Subsequence of A034707.
A084143(a(n)) > 0, complement of A087072.
Sequence in context: A153663 A065528 A360398 * A084146 A314380 A332513
KEYWORD
nice,nonn,easy
AUTHOR
G. L. Honaker, Jr., Dec 31 1999
EXTENSIONS
More terms from David W. Wilson, Jan 13 2000
STATUS
approved