OFFSET
1,2
COMMENTS
The next term a(6) has been claimed to be 1141, but this is incorrect. In fact, 1141^6 is the sum of seven 6th powers. - Jud McCranie, Jun 10 2007
a(7) = 568 and a(8) = 1409. - J. Lowell, Jul 25 2007
a(6) is either 0 (no solution) or greater than 730000 (see the Resta & Meyrignac link, p. 1054). - Jon E. Schoenfield, Jul 22 2017
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 164.
LINKS
Jean-Charles Meyrignac, FAQ File
Jean-Charles Meyrignac, Resta's Algorithm
Giovanni Resta and Jean-Charles Meyrignac, The smallest solutions to the diophantine equation x^6 + y^6 = a^6 + b^6 + c^6 + d^6 + e^6, Math. Comp. 72 (2003), pp. 1051-1054.
EXAMPLE
1^1 = 1^1.
5^2 = 3^2 + 4^2.
6^3 = 3^3 + 4^3 + 5^3.
353^4 = 30^4 + 120^4 + 272^4 + 315^4.
72^5 = 19^5 + 43^5 + 46^5 + 47^5 + 67^5.
568^7 = 127^7 + 258^7 + 266^7 + 413^7 + 430^7 + 439^7 + 525^7.
1409^8 = 90^8 + 223^8 + 478^8 + 524^8 + 748^8 + 1088^8 + 1190^8 + 1324^8.
PROG
(PARI) A007666(n, s, m, p=n)={ /* Check whether s can be written as sum of n positive p-th powers not larger than m^p. If so, return the base a of the largest term a^p.*/ s>n*m^p && return; n==1&&return(ispower(s, p, &n)*n); /* if s, m, p are not given, s>=n and m are arbitrary and p=n. */ !s&&for(m=round(sqrtn(n, n)), 9e9, A007666(n, m^n, m-1, n)&&return(m)); for(a=ceil(sqrtn(s\n, p)), min(sqrtn(s-n+1, p), m), A007666(n-1, s-a^p, a, p)&&return(a)); } \\ M. F. Hasler, Nov 17 2015
CROSSREFS
KEYWORD
nonn,hard,nice,more
AUTHOR
EXTENSIONS
Name clarified by Dmitry Kamenetsky, Aug 05 2015
STATUS
approved