The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A161885 Smallest k such that n^5 = a_1^5+...+a_k^5 and all a_i are positive integers less than n. 7
32, 26, 19, 18, 14, 12, 9, 11, 9, 13, 6, 12, 8, 10, 9, 8, 10, 10, 9, 10, 10, 7, 6, 9, 7, 9, 8, 9, 6, 9, 6, 8, 7, 7, 6, 8, 7, 8, 7, 7, 7, 9, 8, 9, 7, 8, 6, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 6, 8, 8, 6, 7, 7, 7, 7, 5, 7, 7, 7, 7, 8, 6, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 6, 7, 7, 7, 5, 7, 6, 7, 7, 6, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
Based on Fermat's Last Theorem: 2 never occurs in this sequence. It is not known whether 3 occurs in this sequence. The first time 4 occurs is for 144^5=27^5+84^5+110^5+133^5.
The first time 5, 6, 7, 8, 9, 10 occur is for n=73, 12, 23, 14, 8, 15; see sequence A252485. - M. F. Hasler, Dec 17 2014
LINKS
Eric Weisstein's World of Mathematics, Diophantine Equation 5th Powers
EXAMPLE
a(29) = 9 since 29^5 = 5^5 + 9^5 + 10^5 + 10^5 + 10^5 + 15^5 + 15^5 + 17^5 + 28^5, and there is no sum of less than 9 fifth powers equal to 26^5;
a(30) = 6 since 30^5 = 5^5 + 10^5 + 11^5 + 16^5 + 19^5 + 29^5;
a(72) = 5 since 72^5 = 19^5 + 43^5 + 46^5 + 47^5 + 67^5. - M. F. Hasler, Dec 17 2014
PROG
(PARI) a(n, verbose=0, m=5)={N=n^m; for(k=3, 32, forvec(v=vector(k-1, i, [1, n\sqrtn(k+1-i, m)]), ispower(N-sum(i=1, k-1, v[i]^m), m, &K)&&K>0&&!(verbose&&print1("/*"n" "v"*/"))&&return(k), 1))} \\ M. F. Hasler, Dec 17 2014
(PARI) a(n)={
my(N=n^5, k=3);
while(1,
my(v=vector(k-1, i, [sqrtnint(max((N-(k-i)*(n-1)^5-1)\i, 0), 5)+1, sqrtnint((N-i+1)\(k-i+1), 5)]));
forvec(x=v,
my(s=N-sum(i=1, #x, x[i]^5));
if(s>0 && ispower(s, 5), return(k))
,
1
);
k++
);
}; \\ Charles R Greathouse IV, Dec 18 2014
CROSSREFS
Sequence in context: A070627 A028697 A105701 * A100729 A070728 A070619
KEYWORD
nonn
AUTHOR
Dmitry Kamenetsky, Jun 21 2009
EXTENSIONS
a(43)-a(83) from M. F. Hasler, Dec 17 2014
a(77) corrected by Charles R Greathouse IV, Dec 19 2014
a(84)-a(100) from Charles R Greathouse IV, Dec 19 2014
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 15:02 EDT 2024. Contains 372641 sequences. (Running on oeis4.)