A051681 Smallest term of first run of exactly n consecutive integers which are not squarefree.

4, 8, 48, 242, 844, 22020, 217070, 1092747, 8870024, 262315467, 221167422, 47255689915, 82462576220, 1043460553364, 79180770078548, 3215226335143218, 23742453640900972, 125781000834058568

Offset

1,1

References

a(16) was obtained as a result of a team effort by Z. McGregor-Dorsey et al.

Links

Table of n, a(n) for n=1..18.

L. Marmet, First occurrences of square-free gaps and an algorithm for their computation, arXiv preprint arXiv:1210.3829 [math.NT], 2012. See also the author page.

"sikefield3", double-square (2019).

Eric Weisstein's World of Mathematics, Squarefree.

Example

a(5) = 844: 844 = 2^2*211, 845 = 5*13^2, 846 = 2*3^2*47, 847 = 7*11^2, 848 = 2^4*53.

Mathematica

Module[{tb=Table[If[SquareFreeQ[n], 0, 1], {n, 11*10^5}]}, Table[ SequencePosition[ tb, PadRight[{}, k, 1], 1][[All, 1]], {k, 8}]]//Flatten (* The program generates the first 8 terms of the sequence. To generate more, increase the constants for n and k but the program may take a long time to run. *) (* Harvey P. Dale, Mar 24 2022 *)

Prog

(PARI) iscons(x, n)=if (issquarefree(x-1) && issquarefree(x+n), for (k = 0, n-1, if (issquarefree(x+k), return (0)); ); return (1); ); return (0);
a(n) = {my(x = 1); while (! iscons(x, n), x++); x; } \\ Michel Marcus, Jan 13 2014

Crossrefs

Cf. A045882 (another version), A013929, A053806.

Sequence in context: A078236 A054881 A045882 * A267987 A056407 A329942

Adjacent sequences: A051678 A051679 A051680 * A051682 A051683 A051684

Keyword

nice,nonn,hard,more

Author

Louis Marmet (louis(AT)marmet.org) and David Bernier (ezcos(AT)yahoo.com)

Extensions

a(16) reported by Louis Marmet (louis(AT)marmet.org), Jul 24 2000

a(17) was obtained as a result of a team effort by E. Wong et al.

a(18) = 125781000834058568 was obtained as a result of a team effort by L. Marmet et al.

Status

approved