A063736 - OEIS

A063736

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.

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

EXAMPLE

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

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

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

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

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

CROSSREFS

Cf. A007675, A063838, A008966.