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Primes which are not the sum of consecutive composite numbers.
4

%I #24 Aug 21 2023 15:01:56

%S 2,3,5,7,11,13,47,61,73,107,167,179,313,347,421,479,719,863,1153,1213,

%T 1283,1307,1523,3467,3733,4007,4621,4787,5087,5113,5413,7523,7703,

%U 9817,10333,12347,12539,13381,17027,18553,19717,19813,23399,26003,31873,36097,38833

%N Primes which are not the sum of consecutive composite numbers.

%C It seems reasonable that a(n)/A079149(n) has an asymptote that could be estimated. - _Peter Munn_, Aug 21 2023

%H T. D. Noe, <a href="/A037174/b037174.txt">Table of n, a(n) for n = 1..3492</a> (terms less than 2*10^9)

%p N:= 5000:

%p primes,comps:= selectremove(isprime,{$2..N}):

%p M:= nops(comps):

%p X:= primes:

%p for n from 1 to floor(sqrt(2*N)) do

%p i:= 1;

%p T:= add(comps[k],k=1..n);

%p while T <= N do

%p X := X minus {T};

%p if i + n > M then break fi;

%p T := T + comps[i+n] - comps[i];

%p i := i+1;

%p od;

%p od:

%p X;

%p # _Robert Israel_, Jun 24 2008

%Y Subsequence of A079149.

%Y With {1}, the complement of A133576.

%Y 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).

%Y Cf. A050940, A197227.

%K nonn

%O 1,1

%A _Naohiro Nomoto_

%E More terms from _Jud McCranie_, Jul 12 2000

%E Corrected by _T. D. Noe_, Aug 15 2008