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A058185 Numbers (written in decimal) which appear the same when written in base 5 and base 10/2.

%I A058185 #11 Aug 02 2025 06:26:23
%S A058185 0,1,2,3,4,10,11,12,13,14,20,21,22,23,24,50,51,52,53,54,60,61,62,63,
%T A058185 64,70,71,72,73,74,100,101,102,103,104,110,111,112,113,114,120,121,
%U A058185 122,123,124,250,251,252,253,254,260,261,262,263,264,270,271,272,273,274
%N A058185 Numbers (written in decimal) which appear the same when written in base 5 and base 10/2.
%C A058185 To represent a number in base b, if a digit exceeds b-1, subtract b and carry 1. In fractional base b/c, subtract b and carry c. The sequence consists of numbers which in base 5 only have even digits, or one more than such numbers.
%H A058185 Amiram Eldar, <a href="/A058185/b058185.txt">Table of n, a(n) for n = 1..10000</a>
%H A058185 <a href="/index/Ba#base_fractional">Index entries for sequences related to fractional bases</a>.
%e A058185 10 is a term since it is written as 20 both in base 5 and base 10/2.
%e A058185 40 it not a term since it is written as 130 in base 5 and 80 in base 10/2.
%t A058185 s[n_] := s[n] = If[n == 0, 0, 10 * s[2 * Floor[n/10]] + Mod[n, 10]]; q[k_] := s[k] == FromDigits[IntegerDigits[k, 5]]; Select[Range[0, 300], q] (* _Amiram Eldar_, Aug 02 2025 *)
%o A058185 (PARI) s(n) = if(n == 0, 0, 10 * s(n\10 * 2) + n % 10);
%o A058185 isok(k) = s(k) == fromdigits(digits(k, 5)); \\ _Amiram Eldar_, Aug 02 2025
%Y A058185 Cf. A007091, A024657, A058186.
%K A058185 base,nonn,easy
%O A058185 1,3
%A A058185 _Henry Bottomley_, Nov 17 2000
%E A058185 Offset corrected by _Amiram Eldar_, Aug 02 2025