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 A268337 Numbers which have only digits 0 and 1 in bases 3 and 5. 1
 0, 1, 30, 31, 756, 3250, 3276, 3280, 81255, 81256, 81280, 81900, 81901, 82000, 59078250, 59078251, 59078280, 59078281, 31789468750, 31789468776, 31789469505, 31789469506, 31789471900, 31789471905, 31789471906, 31789472005, 946095722031, 946095800025, 946095800026, 946095800031, 946095800130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The number 82000 is famous for having only digits 0 and 1 in all bases <= 5, no other such number > 1 is known. See also A146025 and A258981. If explicit formulas for (convenient) infinite subsequences of this one can be found, this could open new ways to progress on this problem. The terms come in groups having roughly the first half (or at least third) of digits in common, see the link "Terms in base 10, 5 and 3". LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 (first 84 terms from M. F. Hasler, next 31 terms from Charles R Greathouse IV) M. F. Hasler, Terms in base 10, 5 and 3. FORMULA a(n) >> n^k with k = log 5/log 2 = 2.321928.... - Charles R Greathouse IV, Feb 02 2016 MAPLE d:= 20: # to get all terms < 5^d res:= NULL: T:= combinat:-cartprod([[\$0..1]\$d]): while not T[finished] do   r:= T[nextvalue]();   v:= add(r[i]*5^(d-i), i=1..d);   if max(convert(v, base, 3)) <= 1 then     res:= res, v   fi od: res; # Robert Israel, Feb 01 2016 PROG (PARI) print1(0); for(n=1, 1e10, vecmax(digits(t=subst(Pol(binary(n)), 'x, 5), 3))<2&&print1(", "t)) (PARI) list(lim)=my(v=List([0]), d=digits(lim\1, 5), t); for(i=1, #d, if(d[i]>1, for(j=i, #d, d[j]=1); break)); for(n=1, fromdigits(d, 5), t=fromdigits(binary(n), 5); if(vecmax(digits(t, 3))<2, listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Feb 02 2016 CROSSREFS Cf. A005836, A033042. Sequence in context: A042850 A042852 A042854 * A042856 A042857 A042858 Adjacent sequences:  A268334 A268335 A268336 * A268338 A268339 A268340 KEYWORD nonn,base AUTHOR M. F. Hasler, Feb 01 2016 STATUS approved

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Last modified April 22 12:53 EDT 2021. Contains 343177 sequences. (Running on oeis4.)