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Patterns of possible squarefree triples of 3 consecutive numbers {4k+1, 4k+2, 4k+3} are coded as follows: compute A008966(x) getting one of {000, 001, 010, 011, 100, 101, 110, 111} and convert to decimal.
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%I #15 Aug 18 2024 20:12:10

%S 7,7,3,7,5,7,2,7,7,7,7,3,1,5,7,6,7,7,6,7,3,7,5,7,4,7,7,7,7,3,3,1,7,6,

%T 7,7,6,5,3,7,5,7,2,6,7,7,7,3,7,5,7,6,7,7,7,7,3,7,5,7,4,3,5,7,7,3,7,5,

%U 6,6,7,7,3,5,3,7,5,7,6,7,7,3,7,3,5,4,7,4,7,7,2,7,3,6,5,7,6,7,7,7,7,3,7,5,7

%N Patterns of possible squarefree triples of 3 consecutive numbers {4k+1, 4k+2, 4k+3} are coded as follows: compute A008966(x) getting one of {000, 001, 010, 011, 100, 101, 110, 111} and convert to decimal.

%C All code values arise corresponding to 8 classes of patterns. E.g., the first nonsquarefree triple (000 pattern, code=0) appears at 844, [845, 846, 847], 848 as a middle part of a nonsquarefree 5-tuple. Start values of code=7 triples are listed in A063238.

%F a(n) = 4*A008966(4n+1)+2*A008966(4n+2)+A008966(4n+3).

%e a(0) = 4*A008966(1)+2*A008966(2)+A008966(3) = 4+2+1 = 7.

%e a(11) = 4*A008966(45)+2*A008966(46)+A008966(47) = 0+2+1 = 3.

%e a(12) = 4*A008966(49)+2*A008966(50)+A008966(51) = 0+0+1 = 1.

%e a(13) = 4*A008966(53)+2*A008966(54)+A008966(55) = 4+0+1 = 5.

%e a(14) = 4*A008966(57)+2*A008966(58)+A008966(59) = 4+2+1 = 7.

%Y Cf. A007675, A063838, A008966.

%K nonn

%O 0,1

%A _Labos Elemer_, Aug 24 2001