A063736 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.

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

Offset

0,1

Comments

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.

Links

Table of n, a(n) for n=0..104.

Formula

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,

Example

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}.

Crossrefs

Cf. A007675, A063838, A008683.

Sequence in context: A197846 A153102 A155959 * A212299 A193751 A290565

Adjacent sequences: A063733 A063734 A063735 * A063737 A063738 A063739

Keyword

nonn

Author

Labos Elemer, Aug 24 2001

Status

approved