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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A076440 n which appear to have a unique representation as the difference of two perfect powers and one of those powers is odd; that is, there is only one solution to Pillai's equation a^x - b^y = n, with a>0, b>0, x>1, y>1 and that solution has odd x or odd y (or both odd). 3
1, 2, 10, 30, 38, 46, 122, 126, 138, 142, 146, 150, 154, 166, 170, 190, 194, 214, 222, 234, 270, 282, 298, 318, 338, 342, 354, 370, 382, 386, 406, 486, 490, 498, 502, 518, 546, 550, 566, 574, 582, 586, 594, 638, 666, 678, 686, 694, 710, 726, 730, 734, 746 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

There are two types of unique solutions. See A076438 for the general case. This sequence was found by examining all perfect powers (A001597) less than 2^63-1. By examining a larger set of perfect powers, we may discover that some of these numbers do not have a unique representation.

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, D9.

T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, 1986.

LINKS

Table of n, a(n) for n=1..53.

M. E. Bennett, On Some Exponential Equations Of S. S. Pillai,Canad. J. Math. 53 (2001), 897-922.

T. D. Noe, Unique solutions to Pillai's Equation requiring an odd power for n<=1000

Eric Weisstein's World of Mathematics, Pillai's Conjecture

CROSSREFS

Cf. A001597, A076438, A076439.

Sequence in context: A098425 A098408 A063564 * A047198 A290461 A162524

Adjacent sequences:  A076437 A076438 A076439 * A076441 A076442 A076443

KEYWORD

hard,nonn

AUTHOR

T. D. Noe, Oct 12 2002

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 February 27 18:28 EST 2020. Contains 332307 sequences. (Running on oeis4.)