A244097 a(n) is the smallest k such that the sum of n consecutive values M(k) + M(k+1) + ... + M(k+n-1) is zero, where M(m) is the Moebius (or Möbius) function (A008683).

4, 1, 4, 6, 8, 5, 4, 10, 6, 7, 5, 4, 4, 8, 9, 6, 8, 5, 4, 6, 7, 5, 4, 4, 4, 9, 8, 10, 6, 7, 5, 4, 4, 5, 4, 14, 3, 3, 1, 1, 6, 10, 9, 8, 8, 6, 6, 8, 8, 6, 6, 10, 5, 4, 5, 3, 4, 1, 4, 4, 4, 5, 3, 26, 1, 4, 24, 10, 9, 8, 17, 6, 16, 13, 12, 15, 10, 9, 8, 10, 6, 7

Offset

1,1

Links

Michel Lagneau, Table of n, a(n) for n = 1..1000

Example

a(1)= 4 => M(4) = 0;
a(2)= 1 => M(1)+ M(2) = 1-1 = 0;
a(3)= 4 => M(4)+ M(5)+ M(6) = 0-1+1 = 0;
a(4)= 6 => M(6)+ M(7)+ M(8) + M(9) = 1-1+0+0 = 0;
a(5)= 8 => M(8)+ M(9)+ M(10)+ M(11)+ M(12) = 0+0+1-1+0 = 0.

Mathematica

Table[k=1; While[Sum[MoebiusMu[k+i], {i, 0, n-1}]!=0, k++]; k, {n, 1, 100}]

Prog

(PARI) a(n) = my(k = 1); while(sum(j=k, n+k-1, moebius(j)) != 0, k++); k; \\ Michel Marcus, Aug 30 2014

Crossrefs

Cf. A008683, A171910.

Sequence in context: A092856 A051006 A072812 * A162956 A131112 A141225

Adjacent sequences: A244094 A244095 A244096 * A244098 A244099 A244100

Keyword

nonn

Author

Michel Lagneau, Aug 30 2014

Status

approved