cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A020755 Increasing gaps between squarefree numbers (upper end).

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%I A020755 #17 Mar 17 2025 07:02:41
%S A020755 2,5,10,51,246,849,22026,217077,1092755,8870033,221167433,47255689927,
%T A020755 82462576233,1043460553378,79180770078563,3215226335143234,
%U A020755 23742453640900989,125781000834058586
%N A020755 Increasing gaps between squarefree numbers (upper end).
%C A020755 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
%F A020755 a(n) = A020754(n) + A020753(n). - _M. F. Hasler_, Dec 28 2015
%e A020755 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.
%o A020755 (PARI) A020755(n)=for(k=L=1,oo,issquarefree(k)||next;k-L>=n&&return(k);L=k) \\ _M. F. Hasler_, Dec 28 2015
%Y A020755 Cf. A005117, A020754, A020753, A045882, A051681.
%K A020755 nonn,hard
%O A020755 1,1
%A A020755 _David W. Wilson_
%E A020755 Thanks to Christian Bower for additional comments.
%E A020755 More terms (computed using data from A020754) added by _M. F. Hasler_, Dec 28 2015