OFFSET
1,3
COMMENTS
Where is there a proof that this sequence is infinite? - Carlos Rivera, Apr 17 2002
Moser shows that the average order of A054845 is log(2), and hence this sequence is infinite with lower density at least 1 - log 2 = 0.306.... - Charles R Greathouse IV, Mar 21 2011
LINKS
Franklin T. Adams-Watters, Table of n, a(n) for n = 1..10001
Leo Moser, Notes on number theory. III. On the sum of consecutive primes, Canad. Math. Bull. 6 (1963), pp. 159-161.
FORMULA
A054845(a(n)) = 0. - Ray Chandler, Sep 20 2023
EXAMPLE
The number 14 cannot be expressed as a sum of any consecutive subset of the following primes: {2, 3, 5, 7, 11, 13}.
PROG
(BASIC) 10 N=1 20 N=N+1: if N=prmdiv(N) then goto 20 30 P=1 40 P=nxtprm(P):S=P:Q=P: if S>N\2 then print N; :goto 20 50 Q=nxtprm(Q):S=S+Q 60 if S=N then goto 20 70 if S>N then goto 40 80 goto 50
(PARI) is(n)=if(isprime(n), return(0)); 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(1)); t=vecsum(v); if (t==n, return(0)); 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(1)); if(t==n, return(0))) \\ Charles R Greathouse IV, May 05 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 02 2000
STATUS
approved