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A034707 Numbers that are sums (of a nonempty sequence) of consecutive primes. 21
2, 3, 5, 7, 8, 10, 11, 12, 13, 15, 17, 18, 19, 23, 24, 26, 28, 29, 30, 31, 36, 37, 39, 41, 42, 43, 47, 48, 49, 52, 53, 56, 58, 59, 60, 61, 67, 68, 71, 72, 73, 75, 77, 78, 79, 83, 84, 88, 89, 90, 95, 97, 98, 100, 101, 102, 103, 107, 109, 112, 113, 119, 120, 121, 124, 127 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A050936 is a subsequence (which still includes primes, embodied by A067377). - Enoch Haga, Jun 16 2002, R. J. Mathar, Oct 10 2010
LINKS
Leo Moser, On the Sum of Consecutive Primes. Canad. Math. Bull. 6 (1963), 159-161.
Janyarak Tongsomporn, Saeree Wananiyaku, and Jörn Steuding, Sums of consecutive prime squares, Integers (2022) Vol. 22, #A9.
FORMULA
A054845(a(n)) > 0. - Ray Chandler, Sep 20 2023
MATHEMATICA
f[n_] := Block[{len = PrimePi@ n}, p = Prime@ Range@ len; Count[ Flatten[ Table[ p[[i ;; j]], {i, len}, {j, i, len}], 1], q_ /; Total@ q == n]]; Select[ Range@ 1000, f@ # > 0 &] (* Or quicker for a larger range *)
lmt = 10000; p = Prime@ Range@ PrimePi@ lmt; t = Table[0, {lmt}]; Do[s = 0; j = i; While[s = s + p[[j]]; s <= lmt, t[[s]]++; j++], {i, Length@ p}]; Select[ Range@ lmt, t[[#]] > 0 &]
upto=200; Select[Union[Flatten[Table[ Total/@Partition[Prime[ Range[ PrimePi[ upto]]], n, 1], {n, upto-1}]]], #<=upto&] (* Harvey P. Dale, Jul 15 2011 *)
PROG
(PARI) is(n)=if(isprime(n), return(1)); 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
CROSSREFS
Complement is A050940.
Sequence in context: A266347 A028788 A197128 * A288378 A187909 A156247
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
Updated a misleading comment. - R. J. Mathar, Oct 10 2010
STATUS
approved

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Last modified February 29 17:46 EST 2024. Contains 370428 sequences. (Running on oeis4.)