

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.


1



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
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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 quintuplet. 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} muvalue 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



