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)
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 };
CROSSREFS
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