cp's OEIS Frontend

A101439 Areas of primitive Pythagorean triangles which are palindromes.

%I A101439 #16 Jun 07 2024 14:25:43
%S A101439 6,63336,474474,666666,4383834,43177134,460962269064,60471399317406,
%T A101439 60490233209406,643869171968346,6708875775788076,44703479297430744,
%U A101439 608857707707758806,44523865177156832544,683665820959028566386
%N A101439 Areas of primitive Pythagorean triangles which are palindromes.
%C A101439 Other parts of the n-th triangle are {m,n}, {a,b,c}:
%C A101439 a(1): {1,2}, {3,4,5};
%C A101439 a(2): {8,21}, {377,336,505};
%C A101439 a(3): {1,78}, {6083,156,6085};
%C A101439 a(4): {26,37}, {693,1924,2045};
%C A101439 a(5): {49,62}, {1443,6076,6245};
%C A101439 a(6): {11,158}, {24843,3476,25085};
%C A101439 a(7): {2376,2393}, {81073,11371536,11371825};
%C A101439 a(8): {4569,4858}, {2724403,44392404,44475925};
%C A101439 a(9): {2974,3773}, {5390853,22441804,23080205};
%C A101439 a(10): {5402,6829}, {17453637,73780516,75816845};
%C A101439 a(11): {121,38132}, {1454034783,9227944,1454064065};
%C A101439 a(12): {28407,29336}, {53643247,1666695504,1667558545};
%C A101439 a(13): {16593,35986}, {1019664547,1194231396,1570319845};
%C A101439 a(14): {3168,241339}, {58234476697,1529123904,58254549145};
%C A101439 a(15): {160034,213573}, {20002545173,68357882964,71224307485}.
%F A101439 Intersection of A002113 and A024365. - _M. F. Hasler_, Jun 06 2024
%e A101439 666666 is a member as it is a palindromic number and is the area of a primitive Pythagorean triangle with legs a=693 & b=1924 and hypotenuse c=2045.
%t A101439 lst = {}; Do[ If[ GCD[m, n] == 1, a = IntegerDigits[m*n^3 - n*m^3]; If[ Reverse[a] == a, lst = Sort[ AppendTo[ lst, a]]; Print[{n^2 - m^2, 2m*n, n^2 + m^2, m*n^3 - n*m^3}]]], {n, 55000}, {m, If[ EvenQ[n], 1, 2], n - 1, 2}]; lst (* _Robert G. Wilson v_, Jan 25 2005 *)
%o A101439 (PARI) for(n=2,oo, is_A024365(a=A002113(n)) && print1(a", ")) \\ Could be made to a function returning, e.g., the n-th row := the n-digit terms. - _M. F. Hasler_, Jun 06 2024
%Y A101439 Cf. A101450.
%Y A101439 Cf. A002113, A024365.
%K A101439 nonn,base
%O A101439 1,1
%A A101439 _Zak Seidov_, Jan 18 2005
%E A101439 a(8) & a(10) - a(13) from _Robert G. Wilson v_, Jan 25 2005
%E A101439 a(14) and a(15) from _Ray Chandler_, Feb 10 2013