A077647 Smallest term of a run of at least 8 consecutive integers which are not squarefree.

1092747, 7216618, 8870024, 8870025, 14379271, 22635347, 24816974, 25047846, 33678771, 33908368, 33908369, 34394371, 34682346, 37923938, 49250144, 49250145, 53379270, 69147868, 69147869, 70918820, 70918821, 71927247, 72913022, 83605071, 85972019, 90571646

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

A077647 = { A077640[k] | A077640[k+1] = A077640[k]+1 }. - M. F. Hasler, Feb 01 2016

Example

n=8870024: squares dividing n+j (j=0...8) i.e. 9 consecutive integers are as follows {4,25,121,841,4,49,961,9,16}

Mathematica

s8[x_] := Apply[Plus, Table[Abs[MoebiusMu[x+j]], {j, 0, 7}]] If[Equal[s, 0], Print[n]], {n, 1000000, 100000000}]
Flatten[Position[Partition[SquareFreeQ/@Range[91000000], 8, 1], _?(Union[#]=={False}&), {1}, Heads->False]]

Prog

(PARI) for(n=1, 10^8, forstep(k=7, 0, -1, issquarefree(n+k)&&(n+=k)&&next(2)); print1(n", ")) \\ M. F. Hasler, Feb 03 2016

Crossrefs

Cf. A013929, A051681.

Cf. A045882 (first k-chain), A068781 (2-chains), A070258 (3-chains), A070284 (4-chains), A078144 (5-chains), A049535 (6-chains), A077640 (7-chains), A077647 (8-chains), A078143 (9-chains), A268313 (10-chains), A268314 (11-chains).

Sequence in context: A224592 A252119 A109148 * A172647 A172754 A268036

Adjacent sequences: A077644 A077645 A077646 * A077648 A077649 A077650

Keyword

nonn

Author

Labos Elemer, Nov 18 2002

Status

approved