A037174 Primes which are not the sum of consecutive composite numbers.

2, 3, 5, 7, 11, 13, 47, 61, 73, 107, 167, 179, 313, 347, 421, 479, 719, 863, 1153, 1213, 1283, 1307, 1523, 3467, 3733, 4007, 4621, 4787, 5087, 5113, 5413, 7523, 7703, 9817, 10333, 12347, 12539, 13381, 17027, 18553, 19717, 19813, 23399, 26003, 31873, 36097, 38833

Offset: 1

Author

Naohiro Nomoto

Keywords

• nonn

Comments

It seems reasonable that a(n)/A079149(n) has an asymptote that could be estimated. - Peter Munn, Aug 21 2023

Links

• T. D. Noe, Table of n, a(n) for n = 1..3492 (terms less than 2*10^9)

Crossrefs

Subsequence of A079149.

With {1}, the complement of A133576.

Primes that are the sum of specific numbers of consecutive composite numbers: A060254 (2), A060328 (3), A060329 (4), A060330 (5), A060331 (6), A060332 (7), A060333 (8).

Cf. A050940, A197227.

Programs

Maple

N:= 5000:
primes,comps:= selectremove(isprime,{$2..N}):
M:= nops(comps):
X:= primes:
for n from 1 to floor(sqrt(2*N)) do
i:= 1;
T:= add(comps[k],k=1..n);
while T <= N do
X := X minus {T};
if i + n > M then break fi;
T := T + comps[i+n] - comps[i];
i := i+1;
od;
od:
X;
# Robert Israel, Jun 24 2008

Extensions

More terms from Jud McCranie, Jul 12 2000

Corrected by T. D. Noe, Aug 15 2008