OFFSET
1,1
COMMENTS
An antirun of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by more than one.
Conjecture: The maximum is 9, and there is no antirun of more than 9 nonsquarefree numbers. Confirmed up to 100,000,000.
LINKS
EXAMPLE
Row-lengths of:
4 8
9 12 16 18 20 24
25 27
28 32 36 40 44
45 48
49
50 52 54 56 60 63
64 68 72 75
76 80
81 84 88 90 92 96 98
99
The first maximal antirun of length 9 is the following, shown with prime indices:
6345: {2,2,2,3,15}
6348: {1,1,2,9,9}
6350: {1,3,3,31}
6352: {1,1,1,1,78}
6354: {1,2,2,71}
6356: {1,1,4,49}
6358: {1,5,7,7}
6360: {1,1,1,2,3,16}
6363: {2,2,4,26}
MATHEMATICA
Length/@Split[Select[Range[1000], !SquareFreeQ[#]&], #1+1!=#2&]//Most
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 06 2024
STATUS
approved