login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 18 09:09 EST 2017. Contains 294876 sequences.