

A212223


First a(n) > 1 whose expansions in prime bases 2 to prime(n) have the same sum of digits.


0




OFFSET

1,1


COMMENTS

Case a(1) is trivial since only base p(1)=2 is involved.
Conjecture: the sequence never terminates.
a(7) > 2.3*10^16, if it exists.  Giovanni Resta, Oct 29 2018


LINKS

Table of n, a(n) for n=1..6.


EXAMPLE

a(5) = 1386 because that number has the same sum of digits in the first 5 prime bases 2, 3, 5, 7, 11 (see A212222 and A000040).


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 *)


CROSSREFS

Cf. A212222, A135127, A135121, A037301.
Cf. A000040.
Sequence in context: A130726 A279841 A219195 * A158915 A257478 A243523
Adjacent sequences: A212220 A212221 A212222 * A212224 A212225 A212226


KEYWORD

nonn,base,hard,more


AUTHOR

Stanislav Sykora, May 10 2012


STATUS

approved



