A124967 Numbers which can be expressed as the ordered sum of 3 squares in 3 or more different ways.

41, 50, 54, 65, 66, 74, 81, 86, 89, 90, 98, 99, 101, 110, 113, 114, 117, 121, 122, 125, 126, 129, 131, 134, 137, 145, 146, 149, 150, 153, 161, 162, 164, 166, 169, 170, 171, 173, 174, 178, 179, 181, 182, 185, 186, 189, 194, 197, 198, 200, 201, 205, 206, 209

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

a(1) = 41 because 41 = 4^2+4^2+3^2 or 5^2+4^2+0^2 or 6^2+2^2+1^2.
117=0^2+6^2+9^2=1^2+4^2+10^2=2^2+7^2+8^2, so 117 is in the list.

Maple

b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i^2<n, 0,
      `if`(b(n, i-1, t)>3, 3, min(3, b(n, i-1, t)+
      `if`(i^2>n, 0, b(n-i^2, i, t-1))))))
    end:
a:= proc(n) option remember; local k;
      for k from 1 +`if`(n=1, 0, a(n-1))
      while b(k, isqrt(k), 3)<3 do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 10 2013

Mathematica

Select[Range[210], Length@PowersRepresentations[#, 3, 2] >= 3 &] (* Ray Chandler, Oct 31 2019 *)

Prog

(PARI) isA124967(n)={ local(cnt=0, z2) ; for(x=0, floor(sqrt(n)), for(y=x, floor(sqrt(n-x^2)), z2=n-x^2-y^2 ; if( z2>=y^2 && issquare(z2), cnt++ ; ) ; if(cnt >=3, return(1) ) ; ) ; ) ; return(0) ; } { for(n=1, 200, if( isA124967(n), print1(n, ", ") ; ) ; ) ; } (Mathar)

Crossrefs

Cf. A124966-A124971.

Sequence in context: A039383 A043206 A043986 * A224443 A349779 A261259

Adjacent sequences: A124964 A124965 A124966 * A124968 A124969 A124970

Keyword

nonn

Author

Artur Jasinski, Nov 14 2006

Extensions

Corrected and extended by Ray Chandler and R. J. Mathar, Nov 29 2006

Status

approved