A052199 Numbers that are expressible as the sum of 2 distinct positive squares in more ways than any smaller number.

1, 5, 65, 325, 1105, 5525, 27625, 71825, 138125, 160225, 801125, 2082925, 4005625, 5928325, 29641625, 77068225, 148208125, 243061325, 1215306625, 3159797225, 6076533125, 12882250225, 53716552825, 64411251125, 167469252925, 322056255625, 785817263725

Offset

1,2

References

Donald S. McDonald, Postings to sci.math newsgroup, Feb 21, 1995 and Dec 04, 1995.

Links

Ray Chandler, Table of n, a(n) for n = 1..422

Dirk Frettlöh, "Tile Orientations with Distinct Frequencies", Ch. 1.5 in Aperiodic Order, Vol. 2: Crystallography and Almost Periodicity, 2017, see page 9.

Donald S. McDonald, World Mathematical Year 2000 Poster Competition

G. Xiao, Two squares

Index entries for sequences related to sums of squares

Example

65 = 1^2 + 8^2 = 4^2 + 7^2, the smallest expressible in two ways, so 65 is a term.

Prog

(PARI)
c_old=-1; for(n=1, 10000, c=0; for(i=1, floor(sqrt(n)), for(j=1, i-1, if(i^2+j^2==n, c+=1))); if(c>c_old, print1(n, ", "); c_old=c)) - Derek Orr, Mar 15 2019

Crossrefs

Cf. A001983, A007511, A048610, A071383. Subsequence of A054994. Where records occur in A025441; corresponding number of ways is A060306.

Sequence in context: A234335 A071902 A211412 * A093195 A292228 A195579

Adjacent sequences: A052196 A052197 A052198 * A052200 A052201 A052202

Keyword

nonn

Author

Jud McCranie, Jan 28 2000

Extensions

More terms from Randall L Rathbun, Jan 18 2002

Edited by Ray Chandler, Jan 12 2012

Status

approved