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A050940
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Numbers that are not the sum (of a nonempty sequence) of consecutive primes.
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5
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0, 1, 4, 6, 9, 14, 16, 20, 21, 22, 25, 27, 32, 33, 34, 35, 38, 40, 44, 45, 46, 50, 51, 54, 55, 57, 62, 63, 64, 65, 66, 69, 70, 74, 76, 80, 81, 82, 85, 86, 87, 91, 92, 93, 94, 96, 99, 104, 105, 106, 108, 110, 111, 114, 115, 116, 117, 118, 122, 123, 125
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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The number 14 cannot be expressed as a sum of any consecutive subset of the following primes: {2, 3, 5, 7, 11, 13}.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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