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A212223 First a(n) > 1 whose expansions in prime bases 2 to prime(n) have the same sum of digits. 0
2, 6, 6, 882, 1386, 2007986541 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Case a(1) is trivial since only base p(1)=2 is involved.

Conjecture: the sequence never terminates.

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

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Last modified June 28 16:43 EDT 2017. Contains 288839 sequences.