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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 16 12:45 EDT 2021. Contains 345057 sequences. (Running on oeis4.)