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.

A303500 The smallest positive even integer that can be written with n digits in base 3/2.

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%I A303500 #74 Jul 03 2021 07:58:58
%S A303500 2,21,210,2101,21011,210110,2101100,21011000,210110001,2101100011,
%T A303500 21011000110,210110001101,2101100011010,21011000110100,
%U A303500 210110001101001,2101100011010011,21011000110100110,210110001101001101
%N A303500 The smallest positive even integer that can be written with n digits in base 3/2.
%C A303500 a(n) is a prefix of a(n+1).
%C A303500 The smallest, not necessarily even, integer in base 3/2 with n digits is a(n-1) with 0 added at the end.
%H A303500 B. Chen, R. Chen, J. Guo, S. Lee et al., <a href="http://arxiv.org/abs/1808.04304">On Base 3/2 and its Sequences</a>, arXiv:1808.04304 [math.NT], 2018.
%F A303500 a(n) = A024629(A305498(n)). - _R. J. Mathar_, Jun 25 2018
%e A303500 The number 5 in base 3/2 is 22, and the number 6 is 210. Therefore, 210 is the smallest even integer with 3 digits in base 3/2.
%p A303500 roll32 := proc(L)
%p A303500     local piv,L1 ;
%p A303500     piv := 1;
%p A303500     L1 := subsop(piv=op(piv,L)+1,L) ;
%p A303500     while op(piv,L1) >= 3 do
%p A303500         L1 := [seq(0,i=1..piv), op(piv+1,L1)+1, seq(op(i,L1),i=piv+2..nops(L1))] ;
%p A303500         piv := piv+1 ;
%p A303500     end do:
%p A303500     L1 ;
%p A303500 end proc:
%p A303500 from32 := proc(L)
%p A303500     add( op(i,L)*(3/2)^(i-1),i=1..nops(L)) ;
%p A303500 end proc:
%p A303500 A303500 := proc(n)
%p A303500     local dgs ;
%p A303500     dgs := [seq(0,i=1..n-1),1] ;
%p A303500     while not type(from32(dgs),'even') do
%p A303500         dgs := roll32(dgs) ;
%p A303500     end do:
%p A303500     dgs := ListTools[Reverse](dgs) ;
%p A303500     digcatL(%) ;
%p A303500 end proc: # _R. J. Mathar_, Jun 25 2018
%Y A303500 See A024629 for the base-3/2 expansion of n.
%Y A303500 Cf. also A304024, A304025, A070885, A304272, A081848, A246435, A005428, A073941.
%K A303500 nonn,base
%O A303500 0,1
%A A303500 _Tanya Khovanova_ and PRIMES STEP Senior group, May 09 2018