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A034707 Numbers that are sums of consecutive primes. 14
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

T. D. Noe, Table of n, a(n) for n = 1..10000

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.

Cf. A050936, A054845.

Sequence in context: A266347 A028788 A197128 * A288378 A187909 A156247

Adjacent sequences:  A034704 A034705 A034706 * A034708 A034709 A034710

KEYWORD

nonn,nice,easy

AUTHOR

Erich Friedman

EXTENSIONS

Updated a misleading comment. - R. J. Mathar, Oct 10 2010

STATUS

approved

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Last modified September 24 18:54 EDT 2017. Contains 292433 sequences.