cp's OEIS Frontend

A317777 Numbers whose digital sums in bases 2, 3, 4, and 5 are all equal.

%I A317777 #32 Dec 14 2024 11:07:54
%S A317777 1,23162843828305,5722224662500629,25185954575304707081301,
%T A317777 407805072367801818857674005,1705412607407578552438012746487125,
%U A317777 1705412607426764386750185803694405,1705412607426764386750185803695125,1705412607426764386750186877112645,1705412607431411795338502226662661
%N A317777 Numbers whose digital sums in bases 2, 3, 4, and 5 are all equal.
%C A317777 Comment from _Max Alekseyev_, Dec 11 2024 (Start)
%C A317777 The beginning of the sequence suggests that the terms may be rather sparse.
%C A317777 However, as terms become larger, they tend to appear in unexpected constellations such as:
%C A317777    89675268900935540640454882129695060
%C A317777    89675268900935540640454882129695061
%C A317777    89675268900935540640454933652788500
%C A317777    89675268900935540640454933652788501
%C A317777    89675273848747799396737823490250005
%C A317777 or
%C A317777    113343080811409868866589092414267671876
%C A317777    113343080811409868866589092414267671877
%C A317777    113343080811409868867743138448975156500
%C A317777    113343080811409868867743138448975156501
%C A317777    113343080811409868867760032719746187600
%C A317777    113343080811409868867760032719746187601
%C A317777    113343080811409868867760239410949735765
%C A317777    113343080811409868867761158326773437508
%C A317777    113343080811409868867761158326773437509
%C A317777 I can explain when two terms differ by 1, where the first one happens to end with a digit < b-1 for each base b in {2,3,4,5}, but the above constellations are a total mystery.
%C A317777 (End)
%H A317777 Max Alekseyev, <a href="/A317777/b317777.txt">Table of n, a(n) for n = 1..28</a>
%e A317777 23162843828305 in bases 2, 3, 4, and 5 is equal to 101010001000100000101000101000001000001010001, 10001000100100102010101011001, 11101010011011001001101, and 11014000001010001210, respectively. The sum of the digits is 13 in all four cases.
%Y A317777 Subsequence of A037301 and A135122.
%Y A317777 Cf. A317725.
%K A317777 nonn,base,hard
%O A317777 1,2
%A A317777 _Giovanni Resta_, Aug 06 2018
%E A317777 Terms a(5) onward from _Max Alekseyev_, Sep 09 2023