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 A225760 Counts of internal lattice points within more than one primitive Pythagorean triangle (PPT). 0
 2287674594, 983574906769, 16155706018465, 24267609913869, 72461523834219, 367110963344658, 473161567692022 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A PPT can be drawn as a closed lattice polygon with the hypotenuse intersecting no lattice points other than at its start and end. Consequently the PPT is subject to Pick's theorem. LINKS Eric W. Weisstein, MathWorld: Pick's Theorem Wikipedia, Pick's theorem FORMULA If integers a < b are the perpendicular sides of a PPT, then Pick's theorem gives the count of internal lattice points, I = (a-1)*(b-1)/2 and is comparable to the area, A = a*b/2. EXAMPLE a(1) = 2287674594 as it is the first count of internal lattice points within more than one PPT. It has (a, b) = (18108, 252685) and (28077, 162964). MATHEMATICA getpairs[k_] := Reverse[Select[IntegerPartitions[k, {2}], GCD[#[], #[]]==1 &]]; getlist[j_] := (newlist=getpairs[j]; Table[(newlist[[m]][]^2-newlist[[m]][]^2-1) (2newlist[[m]][]*newlist[[m]][]-1)/2, {m, 1, Length[newlist]}]); maxterms=4000; table=Sort[Flatten[Table[getlist[2p+1], {p, 1, 2maxterms}]]]; n=1; table1={}; While[n>valuation(n, 2), a, if(gcd(b=N/a+1, a+1)==1 && issquare(b^2+(a+1)^2) && s++>1, return(1))); 0 \\ Charles R Greathouse IV, May 15 2013 CROSSREFS Cf. A024407, A225414. Sequence in context: A224988 A327056 A180688 * A022240 A251490 A277720 Adjacent sequences:  A225757 A225758 A225759 * A225761 A225762 A225763 KEYWORD nonn,more AUTHOR Frank M Jackson, May 15 2013 STATUS approved

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Last modified July 11 14:11 EDT 2020. Contains 335626 sequences. (Running on oeis4.)