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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A016078 Smallest number that is sum of 2 positive n-th powers in 2 different ways. 3
4, 50, 1729, 635318657 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(5) > 10^23. - Jon E. Schoenfield, Apr 19 2014

REFERENCES

R. Alter, Computations and generalizations on a remark of Ramanujan, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981.

LINKS

Table of n, a(n) for n=1..4.

FORMULA

a(n) <= A230561(n) for n > 1, with equality at least for n = 2, and inequality at least for n = 3. - Jonathan Sondow, Oct 24 2013

EXAMPLE

4=1^1+3^1=2^1+2^1, 50=1^2+7^2=5^2+5^2, 1729=1^3+12^3=9^3+10^3, 635318657 = 59^4+158^4 = 133^4+134^4, etc.

MATHEMATICA

(* This is just an empirical verification *) Do[max = 4 + n^4; Clear[cnt]; cnt[_] = 0; smallest = Infinity;  Do[ cnt[an = x^n + y^n] += 1; If[cnt[an] == 2 && an < smallest, smallest = an], {x, 1, max}, {y, x, max}]; Print["a(", n, ") = ", smallest], {n, 1, 4}] (* Jean-François Alcover, Aug 13 2013 *)

CROSSREFS

Cf. A046881, A230561.

Sequence in context: A201829 A201209 A026865 * A231832 A193157 A235604

Adjacent sequences:  A016075 A016076 A016077 * A016079 A016080 A016081

KEYWORD

nonn,nice,hard,more

AUTHOR

Robert G. Wilson v, Dec 11 1999

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 23 22:48 EST 2014. Contains 249866 sequences.