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%I #11 Aug 21 2023 08:22:43
%S 23,31,41,59,67,71,109,113,131,139,157,199,211,239,251,269,293,311,
%T 337,379,383,409,419,487,491,499,503,521,571,599,631,701,751,769,773,
%U 787,829,877,881,919,941,953,991,1009,1013,1039,1049,1061,1103,1117,1151
%N Primes which are the sum of three consecutive composite numbers.
%C "Consecutive" necessarily means consecutive in the list of composite numbers as opposed to consecutive in the integers, as the sum of any 3 consecutive integers is a multiple of 3. - _Peter Munn_, Aug 20 2023
%e a(3) = 41 is equal to 12+14+15.
%t composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); b = {}; Do[ p = composite[ n ] + composite[ n + 1 ] + composite[ n + 2 ]; If[ PrimeQ[ p ], b = Append[ b, p ] ], {n, 1, 1000} ]; b
%Y Primes that are the sum of other numbers of consecutive composite numbers: A060254 (2), A060329 (4), A060330 (5), A060331 (6), A060332 (7), A060333 (8). See also A037174.
%Y Cf. A034962.
%Y Complement within A166039\{5, 11} of A151741.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Mar 30 2001
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