OFFSET
1,1
COMMENTS
In other words, integers k where an integer b with 1 < b < k exists such that row k of A067255 gives the digits of the base-b expansion of k.
Clearly, all terms are even, since all expansions start with a nonzero digit and thus the factorization of each term contains the prime 2.
EXAMPLE
The base-4 expansion of 200 is 3020. 2^3 * 3^0 * 5^2 * 7^0 = 200, so 200 is a term of the sequence.
MATHEMATICA
base[n_] := Block[{e, t=0, m, b=0, s=False, p, x, pp}, pp = PrimePi@ FactorInteger[n][[-1, 1]]; If[2^(pp - 1) > n, 0, e = IntegerExponent[n, Prime@ Range@ pp]; m = Max[e] + 1; p = Total[Reverse[e] x^Range[0, Length[e] - 1]]; While[((p x^t) /. x -> m ) <= n, s = Reduce[p x^t == n && m <= x < n, x, Integers]; If[s === False, t++, b = x /. List[ToRules@ s][[1]]; Break[], t++]]; b]]; Select[Range[4, 10^5, 2], base[#] > 0 &] (* Giovanni Resta, Apr 10 2019 *)
PROG
(PARI) is(n) = for(b=2, n-1, my(d=digits(n, b), k=#d, x=1); while(k > 0, x=x*prime(k)^d[k]; k--); if(x==n, return(1))); 0
for(t=1, oo, if(is(2*t), print1(2*t, ", ")))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Felix Fröhlich, Apr 09 2019
EXTENSIONS
a(21)-a(40) from Giovanni Resta, Apr 10 2019
STATUS
approved