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 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

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Last modified April 10 14:07 EDT 2021. Contains 342845 sequences. (Running on oeis4.)