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

1,1

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)

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

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.

Sequence in context: A228199 A128292 A140464 * A238851 A037949 A110600

Adjacent sequences: A037171 A037172 A037173 * A037175 A037176 A037177

Keyword

nonn

Author

Naohiro Nomoto

Extensions

More terms from Jud McCranie, Jul 12 2000

Corrected by T. D. Noe, Aug 15 2008

Status

approved