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Search: id:A063736
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| A063736 |
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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. |
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+0
2
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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All code values arise corresponding to 8 classes of patterns. E.g. the first non-squarefree triple (000 pattern, code=0) appears at 844, [845, 846, 847], 848 as a middle part of a non-squarefree quintuplet. Start values of code=7 triples are listed in A063238.
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FORMULA
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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,
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EXAMPLE
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Three consecutive squarefree number give (1, 1, 1) pattern providing code=7; while 3 consecutive non-squarefree 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}.
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CROSSREFS
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Cf. A007675, A063838, A008683.
Sequence in context: A136141 A155959 A153102 this_sequence A153204 A136478 A097903
Adjacent sequences: A063733 A063734 A063735 this_sequence A063737 A063738 A063739
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Aug 24 2001
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