A272119 Values of a^2 + b^2 such that the equation (a^2 + b^2)^2 = x^2 + y^2 + z^2 is soluble where a, b, x, y, z are nonzero integers.

13, 17, 18, 25, 26, 29, 34, 37, 41, 45, 50, 52, 53, 58, 61, 65, 68, 72, 73, 74, 82, 85, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 122, 125, 130, 136, 137, 145, 146, 148, 149, 153, 157, 162, 164, 169, 170, 173, 178, 180, 181, 185, 193, 194, 197, 200, 202, 205, 208, 212, 218

Offset

1,1

Comments

52 is the first term that is not a member of A046711.

Links

Table of n, a(n) for n=1..63.

Example

13 is a term because 13 = 2^2 + 3^2 and 13^2 = 3^2 + 4^2 + 12^2.

Prog

(PARI) isA000404(n) = {for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}
isA000408(n) = {my(a, b) ; a=1 ; while(a^2+1<n, b=1 ; while(b<=a && a^2+b^2<n, if(issquare(n-a^2-b^2), return(1) ) ; b++ ; ) ; a++ ; ) ; return(0); }
lista(nn) = for(n=1, nn, if(isA000404(n) && isA000408(n^2), print1(n, ", ")));

Crossrefs

Cf. A000404, A000408, A046711.

Sequence in context: A338371 A117326 A052055 * A075761 A046064 A322274

Adjacent sequences: A272116 A272117 A272118 * A272120 A272121 A272122

Keyword

nonn,easy

Author

Altug Alkan, Apr 21 2016

Status

approved