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.
%I A185456 #23 Dec 06 2019 21:43:32 %S A185456 1,3,5,8,9,14,15,16,17,26,27,28,29,30,31,32,33,50,51,52,53,54,55,56, %T A185456 57,58,59,60,61,62,63,64,65,98,99,100,101,102,103,104,105,106,107,108, %U A185456 109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124 %N A185456 Payphone packing sequence. %C A185456 Assume that the first person to use a bank of payphones selects one at the end, and all subsequent users select the phone which puts them farthest from the current phone users. U(n) is the smallest number of phones such that n may be used without any two adjacent phones being used. %F A185456 a(n) is the index of the n-th record in A166079, which is given by the recurrence y(n) = y(m) + y(n-m+1) - 1, with y(1) = y(2) = 1 and y(3) = 2, where m = ceiling(n/2). - _John W. Layman_, Feb 05 2011 %F A185456 From _Nathaniel Johnston_, Apr 12 2011: (Start) %F A185456 a(n) = a(n-1) + n - 1 if n = 2^k + 2 for some natural number k, a(n) = a(n-1) + 1 otherwise, for n >= 3. %F A185456 a(n) = n + 2^(1+floor(log_2(n-2))) for n >= 3. (End) %e A185456 For 4 phones, only the outer two will be used. For a fifth phone, however, a third person may come along and use the middle phone without any two being adjacent; thus U(3)=5. A seventh phone will not lead to a fourth being used without adjacent people, but an eighth will, hence U(4)=8. %K A185456 easy,nonn %O A185456 1,2 %A A185456 _Craig B. Daniel_, Feb 04 2011 %E A185456 Terms 26,27,...,114 added by _John W. Layman_, Feb 05 2011 %E A185456 Edited by _N. J. A. Sloane_, Feb 07 2011 %E A185456 a(51) - a(60) from _Nathaniel Johnston_, Apr 12 2011