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A071367 Numbers n such that n+0, n+1, n+2, n+3 and n+4 are, in some order, 1 * a prime, 2 * a prime, 3 * a prime, 4 * a prime and 5 * a prime.

%I A071367 #19 Jul 15 2024 03:29:30
%S A071367 6,211,2305,2731,19441,116131,174595,222931,229945,232051,243091,
%T A071367 266401,334315,350785,423481,495265,523945,530545,535915,539401,
%U A071367 556705,600601,663601,671035,689131,721891,907195,908041,1105105,1113961,1289731
%N A071367 Numbers n such that n+0, n+1, n+2, n+3 and n+4 are, in some order, 1 * a prime, 2 * a prime, 3 * a prime, 4 * a prime and 5 * a prime.
%C A071367 A001221(a(n)) <= 2; A001222(a(n)) <= 3. - _Reinhard Zumkeller_, Aug 01 2015
%H A071367 Reinhard Zumkeller, <a href="/A071367/b071367.txt">Table of n, a(n) for n = 1..1001</a>
%e A071367 211 is a term because 211=1*211, 212=4*53, 213=3*71, 214=2*107 and 215=5*43. The left factors are the integers 1 to 5; and the right factors are primes.
%e A071367 6 is a term because 6=2*3, 7=1*7, 8=4*2, 9=3*3, 10=5*2 where the left factors are the integers 1 to 5 and the right factors are primes. - _Sean A. Irvine_, Jul 14 2024
%o A071367 (Haskell)
%o A071367 a071367 n = a071367_list !! (n-1)
%o A071367 a071367_list = tail $ filter f [1..] where
%o A071367    f x = and $ map g [5, 4 .. 1] where
%o A071367      g k = sum (map h $ map (+ x) [0..4]) == 1 where
%o A071367        h z = if r == 0 then a010051' z' else 0
%o A071367              where (z', r) = divMod z k
%o A071367 -- _Reinhard Zumkeller_, Jul 31 2015
%Y A071367 Cf. A071367 - A071373.
%Y A071367 Cf. A010051, A001221, A001222.
%K A071367 nonn
%O A071367 1,1
%A A071367 _Don Reble_, May 21 2002
%E A071367 Missing 6 inserted by _Sean A. Irvine_, Jul 14 2024