A092357 Smallest value of x=a+b+c+d (a,b,c,d positive integers) such that there are n different values of m=a^2+b^2=c^2+d^2, or 0 if no such x exists.

18, 30, 36, 42, 54, 66, 78, 60, 80, 102, 72, 84, 138, 112, 90, 184, 154, 186, 452, 170, 126, 162, 196, 160, 120, 150, 652, 144, 692, 344, 318, 376, 266, 192, 200, 168, 272, 228, 304, 220, 472, 426, 234, 1052, 1076, 180, 474, 260, 368, 722, 584, 418, 534, 434

Offset

1,1

Comments

This is an infinite sequence because if x=4*p (p=any prime), the number of different n values of m is n=k for p=6k+/-1. I do not know if there is an x for every natural number n.

Links

Table of n, a(n) for n=1..54.

Example

We denote m=a^2+b^2=c^2+d^2 by writing (a,b,c,d). Then:
x=18->(1,7,5,5)=50 for n=1
x=30->(1,12,8,9)=145 (3,11,7,9)=130 for n=2
x=36->(2,14,10,10)=200 (3,14,6,13)=205 (4,13,8,11)=185 for n=3

Crossrefs

Cf. A091459 A090073.

Sequence in context: A151700 A154367 A161164 * A141115 A373844 A039320

Adjacent sequences: A092354 A092355 A092356 * A092358 A092359 A092360

Keyword

nonn

Author

Robin Garcia, Mar 18 2004

Extensions

More terms from Ray Chandler, Mar 26 2004

Status

approved