A135122 -id:A135122 - cp's OEIS frontend

A317725 a(n) is the smallest k > 1 whose sum of digits is the same in all the bases from 2 to n.

2, 6, 21, 23162843828305

Offset: 2

Giovanni Resta, Aug 05 2018

No other terms below 4^60 ~= 1.3*10^36. The sequence is likely finite and complete. - Max Alekseyev, Aug 29 2023

			a(3) = A037301(3).
a(4) = A135122(2).
a(5) = A317777(2) = 23162843828305 in base 2, 3, 4, and 5 is equal to: 101010001000100000101000101000001000001010001, 10001000100100102010101011001, 11101010011011001001101, and 11014000001010001210, respectively. The sum of the digits is 13 in the 4 cases.

Cf. A037301, A135122, A317777.

isok(k, n) = #Set(vector(n-1, b, b++; sumdigits(k, b))) == 1;
a(n) = my(k=2); while (!isok(k, n), k++); k; \\ Michel Marcus, Sep 02 2023

a(2) = 2 prepended by Max Alekseyev, Aug 29 2023

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

Original entry on oeis.org

1, 23162843828305, 5722224662500629, 25185954575304707081301, 407805072367801818857674005, 1705412607407578552438012746487125, 1705412607426764386750185803694405, 1705412607426764386750185803695125, 1705412607426764386750186877112645, 1705412607431411795338502226662661

Offset: 1

Giovanni Resta, Aug 06 2018

Comment from Max Alekseyev, Dec 11 2024 (Start)
The beginning of the sequence suggests that the terms may be rather sparse.
However, as terms become larger, they tend to appear in unexpected constellations such as:
   89675268900935540640454882129695060
   89675268900935540640454882129695061
   89675268900935540640454933652788500
   89675268900935540640454933652788501
   89675273848747799396737823490250005
or
   113343080811409868866589092414267671876
   113343080811409868866589092414267671877
   113343080811409868867743138448975156500
   113343080811409868867743138448975156501
   113343080811409868867760032719746187600
   113343080811409868867760032719746187601
   113343080811409868867760239410949735765
   113343080811409868867761158326773437508
   113343080811409868867761158326773437509
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.
(End)

			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.

Max Alekseyev, Table of n, a(n) for n = 1..28

Subsequence of A037301 and A135122.

Cf. A317725.

Terms a(5) onward from Max Alekseyev, Sep 09 2023

cp's OEIS Frontend

A317725 a(n) is the smallest k > 1 whose sum of digits is the same in all the bases from 2 to n.

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