

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 m1 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



