cp's OEIS Frontend

A124884 Largest number that is not a sum of n distinct primes, or -1 if such a number does not exist.

%I A124884 #9 Mar 31 2012 13:20:33
%S A124884 -1,-1,17,30,41,60,83,102,137,162,203,244,293,334,389,448,515,574,647,
%T A124884 724,803,884,977,1066,1163,1276,1373,1492,1607,1738,1865,2002,2141,
%U A124884 2290,2435,2602,2759,2932,3095,3280,3467,3646,3857,4054,4247,4456,4683,4912,5141,5374
%N A124884 Largest number that is not a sum of n distinct primes, or -1 if such a number does not exist.
%e A124884 a(1) = -1 because there are an infinite number of nonprimes.
%e A124884 a(3) = 17 because 17 = Max[{1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17}] = Max[A124868(n)], where A124868(n) are the natural numbers that are not the sum of 3 distinct primes.
%o A124884 (PARI) print1("-1,-1,");for(n=3,50,L=0;for(i=1,n,L+=prime(i));L*=2;a=matrix(n,L,i,j,0);forprime(p=2,L,forstep(i=n,2,-1,for(j=p+1,L,if(a[i-1,j-p],a[i,j]=1)));a[1,p]=1);r=L;while(a[n,r],r--);print1(r","))
%Y A124884 Number of natural numbers that are not a sum of n distinct primes, or -1 if it is infinite, are listed in A124885(n) = {-1, -1, 12, 22, 34, 49, 68, 90, 117, 147, 180, 219, ...}.
%Y A124884 Natural numbers that are not the sum of 2 distinct primes are {1 - 4, 6, 11, 17, 23, 27, 29, 35, 37, 41, 47, ...}, complement to A038609(n)
%Y A124884 Numbers that are the sum of 2 different primes.
%Y A124884 Natural numbers that are not the sum of 3 distinct primes A124868(n) = {1 - 9, 11, 13, 17}.
%Y A124884 Natural numbers that are not the sum of 4 distinct primes are {1 - 16, 18, 19, 20, 22, 24, 30}.
%Y A124884 Natural numbers that are not the sum of 5 distinct primes are {1 - 27, 29, 31, 32, 33, 35, 37, 41}.
%Y A124884 Natural numbers that are not the sum of 6 distinct primes are {1 - 40, 42, 43, 44, 46, 48, 50, 52, 54, 60}.
%Y A124884 Natural numbers that are not the sum of 7 distinct primes are {1 - 57, 59, 61, 62, 63, 65, 67, 69, 71, 73, 77, 83}.
%Y A124884 Natural numbers that are not the sum of 8 distinct primes are {1 - 76, 78, 79, 80, 82, 84, 85, 86, 88, 90, 92, 94, 96, 100, 102}.
%Y A124884 Natural numbers that are not the sum of 9 distinct primes are {1 - 99, 101, 102, 103, 104, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 131, 133, 137}.
%Y A124884 Natural numbers that are not the sum of 10 distinct primes are {1 - 128, 130, 132, 133, 134, 135, 136, 138, 139, 140, 142, 144, 146, 148, 150, 152, 154, 156, 160, 162}.
%Y A124884 Natural numbers that are not the sum of 11 distinct primes are {1 - 159, 161, 162, 163, 164, 165, 167, 169, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 197, 203}.
%Y A124884 Natural numbers that are not the sum of 12 distinct primes are {1 - 196, 198, 199, 200, 202, 204, 205, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 226, 228, 230, 232, 234, 240, 244}.
%Y A124884 Cf. A000040, A038609, A124868, A124885.
%K A124884 sign
%O A124884 1,3
%A A124884 _Alexander Adamchuk_, Nov 12 2006
%E A124884 a(13)-a(50) from _Robert Gerbicz_, Nov 22 2010