A101439 - OEIS

%I #16 Jun 07 2024 14:25:43

%S 6,63336,474474,666666,4383834,43177134,460962269064,60471399317406,

%T 60490233209406,643869171968346,6708875775788076,44703479297430744,

%U 608857707707758806,44523865177156832544,683665820959028566386

%N Areas of primitive Pythagorean triangles which are palindromes.

%C Other parts of the n-th triangle are {m,n}, {a,b,c}:

%C a(1): {1,2}, {3,4,5};

%C a(2): {8,21}, {377,336,505};

%C a(3): {1,78}, {6083,156,6085};

%C a(4): {26,37}, {693,1924,2045};

%C a(5): {49,62}, {1443,6076,6245};

%C a(6): {11,158}, {24843,3476,25085};

%C a(7): {2376,2393}, {81073,11371536,11371825};

%C a(8): {4569,4858}, {2724403,44392404,44475925};

%C a(9): {2974,3773}, {5390853,22441804,23080205};

%C a(10): {5402,6829}, {17453637,73780516,75816845};

%C a(11): {121,38132}, {1454034783,9227944,1454064065};

%C a(12): {28407,29336}, {53643247,1666695504,1667558545};

%C a(13): {16593,35986}, {1019664547,1194231396,1570319845};

%C a(14): {3168,241339}, {58234476697,1529123904,58254549145};

%C a(15): {160034,213573}, {20002545173,68357882964,71224307485}.

%F Intersection of A002113 and A024365. - _M. F. Hasler_, Jun 06 2024

%e 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 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 (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 Cf. A101450.

%Y Cf. A002113, A024365.

%K nonn,base

%O 1,1

%A _Zak Seidov_, Jan 18 2005

%E a(8) & a(10) - a(13) from _Robert G. Wilson v_, Jan 25 2005

%E a(14) and a(15) from _Ray Chandler_, Feb 10 2013