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A169828
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Numbers n such that the base 2 expansion of n ends with the base 3 expansion of n.
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4
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0, 1, 1002, 1003, 16495194, 16495195, 988496761674, 988496761675, 26688254956950, 26688254956951, 34018805387982, 34018805387983, 18069028755380465688, 18069028755380465689, 38281545036919307556, 38281545036919307557
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OFFSET
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1,3
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COMMENTS
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The entries appear to occur in pairs, (6k, 6k+1). - Zak Seidov, May 31 2010. Proof from Max Alekseyev, May 31 2010: If m is an even term of A169828, then it is also divisible by 3, i.e., m=6k, and m+1 is also a term of A169828. On the other hand, if m is an odd term of A169828, then m == 1 (mod 3) and thus m=6k+1, implying that m-1 is also a term of A169828.
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LINKS
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EXAMPLE
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This is Maple:
convert(1002,base,2);
[0, 1, 0, 1, 0, 1, 1, 1, 1, 1]
convert(1002,base,3);
[0, 1, 0, 1, 0, 1, 1]
988496761674 = 1110011000100110111111111001001101001010 (base 2)
988496761674 = ..............10111111111001001101001010 (base 3)
26688254956950 = 110000100010111010111111101001101010110010110 (base 2)
26688254956950 = ................10111111101001101010110010110 (base 3)
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MAPLE
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f:=proc(n) local t2, t3, i, t0; t0:=1; t2:=convert(n, base, 2); t3:=convert(n, base, 3);
for i from 1 to nops(t3) do if t2[i] <> t3[i] then t0:=-1; fi; od; t0; end;
t4:=[]; for n from 1 to 20000 do if f(n) = 1 then t4:=[op(t4), n]; fi; od: t4;
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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a(11)-a(30) from Max Alekseyev, Jun 01 2010, Sep 21 2016, Aug 26 2020
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STATUS
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approved
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