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 A169828 Numbers n such that the base 2 expansion of n ends with the base 3 expansion of n. 4
 0, 1, 1002, 1003, 16495194, 16495195, 988496761674, 988496761675, 26688254956950, 26688254956951, 34018805387982, 34018805387983, 18069028755380465688, 18069028755380465689, 38281545036919307556, 38281545036919307557, 329813598438369669888, 329813598438369669889, 475572782847745049214, 475572782847745049215 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. LINKS Max Alekseyev, Table of n, a(n) for n = 1..24 Erich Friedman, What's Special About This Number? (See entries 1002, 1003.) EXAMPLE 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) MAPLE 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; CROSSREFS Cf. A175514, A178679, A178680. Sequence in context: A139105 A262596 A213316 * A151956 A111349 A182935 Adjacent sequences:  A169825 A169826 A169827 * A169829 A169830 A169831 KEYWORD base,nonn AUTHOR N. J. A. Sloane, May 30 2010 EXTENSIONS a(5)-a(6) from Zak Seidov and D. S. McNeil, May 31 2010 a(7)-a(8) from Alois P. Heinz, May 31 2010 a(9)-a(12) from Ray Chandler, Jun 01 2010 a(11)-a(20) from Max Alekseyev, Jun 01 2010 a(21)-a(24) from Max Alekseyev, Sep 21 2016 STATUS approved

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