|
| |
|
|
A103266
|
|
Minimal number of squares needed to sum to Fibonacci(n+1).
|
|
3
|
|
|
|
1, 2, 3, 2, 2, 2, 3, 2, 4, 2, 1, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 4, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Since every positive integer is the sum of four squares, no term is greater than 4. Also, since any positive integer not of the form 4^k(8m+7) is the sum 3 or fewer squares, the next occurrences of a(n)=4 are at n = 45, 57, 69, 81, 83, 93, .... - John W. Layman, Mar 30 2005
|
|
|
REFERENCES
|
Hardy and Wright, An Introduction to the Theory of Numbers, Fourth Ed., Oxford, Section 20.10.
|
|
|
LINKS
|
Hans Havermann, Table of n, a(n) for n = 1..1400 (terms 1..465 from Antti Karttunen)
|
|
|
FORMULA
|
a(n) = A002828(A000045(n+1)).
|
|
|
EXAMPLE
|
Fibonacci(10+1) = 89 = 25+64, so a(10)=2.
|
|
|
MATHEMATICA
|
Array[If[First[#] > 0, 1, Length@ First@ Split@ # + 1] &@ SquaresR[Range@ 4, Fibonacci@ #] &, 50, 2] (* Michael De Vlieger, Nov 13 2018, after Harvey P. Dale at A002828 *)
|
|
|
PROG
|
(PARI)
istwo(n:int) = { my(f); if(n<3, return(n>=0); ); f=factor(n>>valuation(n, 2)); for(i=1, #f[, 1], if(bitand(f[i, 2], 1)==1&&bitand(f[i, 1], 3)==3, return(0))); 1 };
isthree(n:int) = { my(tmp=valuation(n, 2)); bitand(tmp, 1)||bitand(n>>tmp, 7)!=7 };
A002828(n) = if(issquare(n), !!n, if(istwo(n), 2, 4-isthree(n))); \\ From A002828
A103266(n) = A002828(fibonacci(1+n)); \\ Antti Karttunen, Nov 10 2018
|
|
|
CROSSREFS
|
Cf. A000045, A002828.
Sequence in context: A324983 A147561 A210659 * A185150 A299229 A289496
Adjacent sequences: A103263 A103264 A103265 * A103267 A103268 A103269
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Giovanni Teofilatto, Mar 20 2005
|
|
|
EXTENSIONS
|
Corrected and extended by John W. Layman, Mar 30 2005
Extended by Ray Chandler, May 16 2005
|
|
|
STATUS
|
approved
|
| |
|
|
