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%I #10 Apr 11 2022 22:21:26
%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 Abs[mu[x]]=am[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) = 4am[4n+1]+2am[4n+2]+am[4n+3], where am[] = Abs[mu[]]; for n = 0, 1, 2 a(n) belong to {1, 2, 3}, (5, 6, 7), (9, 10, 11) numbers,
%e Three consecutive squarefree number give (1, 1, 1) pattern providing code=7; while 3 consecutive nonsquarefree integer between 2 numbers of 4m form results in code=0 because of {0, 0, 0} mu-value pattern. Thus {[45, 46, 47], [49, 50, 51], [53, 54, 55], [57, 58, 59] provide 011, 001, 101, 111 patterns and so 3, 1, 5, 7 codes; a(0)=7 corresponds the start triple={1, 2, 3}.
%Y Cf. A007675, A063838, A008683.
%K nonn
%O 0,1
%A _Labos Elemer_, Aug 24 2001
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