OFFSET
1,1
COMMENTS
Case a(1) is trivial since only base prime(1)=2 is involved.
Conjecture: the sequence never terminates.
a(7) > 2.3*10^16, if it exists. - Giovanni Resta, Oct 29 2018
EXAMPLE
MATHEMATICA
f[n_] := Block[{p = Prime@ Range@ n, k = 2}, While[ Length[ Union[ Total@# & /@ IntegerDigits[k, p]]] != 1, k++]; k] (* Robert G. Wilson v, Oct 24 2014 *)
PROG
(PARI) isok(n, k) = my(s=hammingweight(k)); forprime (b=3, prime(n), if (sumdigits(k, b) != s, return (0))); return (1);
a(n) = my(k=2); while (!isok(n, k), k++); k; \\ Michel Marcus, Jun 08 2021
CROSSREFS
KEYWORD
nonn,base,hard,more
AUTHOR
Stanislav Sykora, May 10 2012
EXTENSIONS
Name edited by Michel Marcus, Sep 14 2020
a(7) from Thomas König, Jun 08 2021
STATUS
approved