login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085634 Numbers of the form 2^a + 3^b = 2^c + 3^d for nonnegative a, b, c, d and a <> c. 3
5, 11, 17, 35, 259 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No more terms < 10^4000. - David Wasserman, Feb 07 2005

LINKS

Table of n, a(n) for n=1..5.

Douglas Edward Iannucci, On duplicate representations as 2^x+3^y for nonnegative integers x and y, arXiv:1907.03347 [math.NT], 2019.

EXAMPLE

a(5) = 256 + 3 = 2^8 + 3^1 = 259 = 16 + 243 = 2^4 + 3^5.

MATHEMATICA

(* Max exponent 8 is sufficient to get all known solutions *)

f[_] = 0; Reap[Do[n = 2^a + 3^b; f[n] = f[n] + 1; If[f[n] == 1, ab[n] = {a, b}, If[f[n] >= 2, Print[HoldForm[2^x + 3^y] /. Thread[{x, y} -> ab[n]], " = ", HoldForm[2^x + 3^y] /. Thread[{x, y} -> {a, b}], " = ", n]; Sow[n]]], {a, 0, 8}, {b, 0, 8}]][[2, 1]] // Union (* Jean-François Alcover, Apr 29 2014 *)

CROSSREFS

Sequence in context: A155030 A030468 A277290 * A157478 A297583 A088903

Adjacent sequences:  A085631 A085632 A085633 * A085635 A085636 A085637

KEYWORD

nonn,more,hard

AUTHOR

Frank Ellermann, Jul 11 2003

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)