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A103246 Numbers y, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers. 2
21, 27, 33, 55, 57, 63, 75, 77, 81, 87, 91, 93, 99, 105, 111, 115, 117, 119, 123, 125, 129, 133, 135, 143, 147, 153, 155, 161, 165, 171, 177, 183, 185, 187, 189, 195, 201, 203, 207, 213, 215, 217, 219, 225, 235, 237, 243, 247, 249, 253, 255, 259, 265, 267, 273 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The example is the smallest such triple in terms of x. In terms of y, 220^2 + 21^2 = 221^2 is the smallest such triple.

Evidently the triples here are ordered so that x is even and y is odd. - Robert Israel, Oct 22 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MathForFun, Title?

EXAMPLE

x=16, y=63, 16^2 + 63^2 = 65^2. 63 is the 6th entry in the list.

MAPLE

N:= 1000: # to get all terms <= N

Res:= NULL:

for m from 1 to N by 2 do

  for n from 1 to m-2 by 2 while m*n <= N do

    if igcd(m, n) > 1 then next fi;

    if not isprime(m*n) and not isprime((m^2+n^2)/2) then

      Res:= Res, m*n;

    fi

od od:

sort(convert({Res}, list)); # Robert Israel, Oct 22 2018

PROG

(PARI) pythtri(n) = { local(a, b, c=0, k, x, y, z, vy, j); w = vector(n*n); for(a=1, n, for(b=1, n, x=2*a*b; y=b^2-a^2; z=b^2+a^2; if(y > 0 &!isprime(x) &!isprime(y) &!isprime(z), if(gcd(x, y)==1&gcd(x, z)==1&gcd(y, z)==1, c++; w[c]=y; ) ) ) ); vy=vector(c); w=vecsort(w); for(j=1, n*n, if(w[j]>0, k++; vy[k]=w[j]; ) ); for(j=1, 200, if(vy[j+1]<>vy[j], print1(vy[j]", ")) ) }

CROSSREFS

Sequence in context: A249729 A280107 A264102 * A206347 A247316 A072392

Adjacent sequences:  A103243 A103244 A103245 * A103247 A103248 A103249

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Mar 19 2005

STATUS

approved

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Last modified May 26 19:26 EDT 2019. Contains 323597 sequences. (Running on oeis4.)