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%I #9 Dec 13 2019 05:21:03
%S 193,277,353,433,443,613,643,653,673,683,739,881,1109,1129,1237,1511,
%T 1531,1609,1619,1697,1873,1999,2017,2027,2113,2207,2239,2281,2371,
%U 2447,2621,2657,2677,2687,2749,2801,2833,2843,2909,2927,3023,3083,3121,3167
%N Primes which are the sum of eight consecutive composite numbers.
%H Robert Israel, <a href="/A060333/b060333.txt">Table of n, a(n) for n = 1..10000</a>
%p comps:= remove(isprime, [$4..1000]):
%p S:= add(comps[i+1..i-8],i=0..7):
%p select(isprime,S); # _Robert Israel_, Dec 12 2019
%t composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); a = {}; Do[ p = Sum[ composite[ n + k ], {k, 0, 7} ]; If[ PrimeQ[ p ], a = Append[ a, p ] ], {n, 1, 600} ]; a
%t Select[Total /@ Partition[ Select[ Range@ 500, CompositeQ], 8, 1], PrimeQ] (* _Giovanni Resta_, Dec 13 2019 *)
%Y Cf. A060254, A060328, A060329, A060330, A060331, A060332, A151738, A151739.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Mar 30 2001
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