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 A049355 #29 Nov 20 2024 08:37:54
%S A049355 75,78,99,108,114,120,135,141,147,156,177,180,198,201,210,216,225,228,
%T A049355 16815,16827,16830,16875,16878,16890,17007,17019,17022,17055,17079,
%U A049355 17085,17115,17118,17127,17133,17142,17145,17259,17262,17274,17307,17310,17319,17325
%N A049355 Digitally balanced numbers in base 4: equal numbers of 0's, 1's, ... 3's.
%C A049355 The sum of reciprocals, Sum_{n>=1} 1/a(n), converges. In general, the sum of the reciprocals of balanced numbers in base b converges for all b >= 4, and diverges for b = 2 or 3 (Papanicolaou, 2013). Grivaux (2015) gives 3 * Sum_{k>=1} (4*k)!/(k!^4 * 4^(4*k)) = 0.857... as an upper bound for this sum. The sum is converging slowly: the sums of the reciprocals of the terms with no more than 4*k digits in base 4, for k = 1, 2, ..., are 0.129.., 0.183..., 0.213..., 0.233..., 0.248..., 0.260..., 0.269..., 0.276..., 0.282..., 0.288..., ... . - _Amiram Eldar_, Feb 15 2024
%H A049355 Harvey P. Dale, <a href="/A049355/b049355.txt">Table of n, a(n) for n = 1..1001</a>
%H A049355 Vassilis Papanicolaou, <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.120.08.754">Problem 11729</a>, The American Mathematical Monthly, Vol. 120, No. 8 (2013), p. 754; <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.122.8.801">Summing the Reciprocals of Normal Numbers Base b</a>, Solution to Problem 11729 by Nicole Grivaux, ibid., Vol. 122, No. 8 (2015), p. 806.
%H A049355 Roberto Tauraso, <a href="https://www.mat.uniroma2.it/~tauraso/AMM/AMM11729.pdf">Problem 11729</a>.
%t A049355 Select[Range[20000],Length[Union[DigitCount[#,4]]]==1&] (* _Harvey P. Dale_, Mar 19 2013 *)
%t A049355 FromDigits[#,4]&/@DeleteCases[Flatten[Permutations/@Table[PadRight[{},4n,{1,0,2,3}],{n,2}],1],_?(#[[1]]==0&)]//Sort (* _Harvey P. Dale_, May 30 2016 *)
%o A049355 (PARI) is(n) = {my(c = matreduce(digits(n,4))[,2]); #c == 4 && #Set(c) == 1;} \\ _Amiram Eldar_, Feb 15 2024
%Y A049355 Cf. A031443.
%Y A049355 Row n = 4 of A378000.
%K A049355 nonn,base
%O A049355 1,1
%A A049355 _Harvey P. Dale_
%E A049355 Offset corrected by _Amiram Eldar_, Feb 15 2024