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

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