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Numbers all of whose base 11 digits are even.
1

%I #18 May 03 2018 09:24:04

%S 0,2,4,6,8,10,22,24,26,28,30,32,44,46,48,50,52,54,66,68,70,72,74,76,

%T 88,90,92,94,96,98,110,112,114,116,118,120,242,244,246,248,250,252,

%U 264,266,268,270,272,274,286,288,290,292,294,296,308,310,312,314,316

%N Numbers all of whose base 11 digits are even.

%C Similar in definition to A033036.

%C As n increases, it is most likely that A212495(n) < A033036(n), although exceptions to this rule can be found. I conjecture that A212495(n) > A033036(n) for only finitely many values of n.

%e 30 is represented by "28" in base 11. Both digits in this representation are even, thus 30 belongs to the sequence.

%t Select[Range[0,350],AllTrue[IntegerDigits[#,11],EvenQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, May 03 2018 *)

%o (PARI) {is(c) = local(d);while(c != 0, d=c%11; c=(c-d)/11; if(d%2==1, return(0))) ; 1}

%o for(i=0, 317, if(is(i), print1(i, ", ")))

%K nonn,base,easy

%O 1,2

%A _Douglas Latimer_, May 18 2012