A020755 Increasing gaps between squarefree numbers (upper end).

2, 5, 10, 51, 246, 849, 22026, 217077, 1092755, 8870033, 221167433, 47255689927, 82462576233, 1043460553378, 79180770078563, 3215226335143234, 23742453640900989, 125781000834058586

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• hard

Comments

Up to n=10, a(n) is the upper end of the first gap of length n. However, for n=11 through n=16, a(n) is the upper end of the first gap of length n+1. See A020753. - M. F. Hasler, Dec 28 2015

Examples

			The first gap in A005117 occurs between 1 and 2 and has length 1. The next largest gap occurs between 3 and 5 and has length 2. The next largest gap is between 7 and 10 and has length 3. Etc. We are only interested in gaps that set new records.
		

Crossrefs

Cf. A005117, A020754, A020753, A045882, A051681.

Programs

PARI

A020755(n)=for(k=L=1,oo,issquarefree(k)||next;k-L>=n&&return(k);L=k) \\ M. F. Hasler, Dec 28 2015

Formula

a(n) = A020754(n) + A020753(n). - M. F. Hasler, Dec 28 2015

Extensions

Thanks to Christian Bower for additional comments.

More terms (computed using data from A020754) added by M. F. Hasler, Dec 28 2015