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

2,1

Comments

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

Links

Table of n, a(n) for n=2..5.

Example

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.

Prog

(PARI) 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

Crossrefs

Cf. A037301, A135122, A317777.

Sequence in context: A368005 A084392 A156155 * A263486 A182544 A216120

Adjacent sequences: A317722 A317723 A317724 * A317726 A317727 A317728

Keyword

nonn,base,hard,more

Author

Giovanni Resta, Aug 05 2018

Extensions

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

Status

approved