The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A121727 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A121727

Hypotenuse of primitive Pythagorean triangles sorted on area (A024406), then on hypotenuse.
(history; published version)

#14 by Ray Chandler at Mon Jun 26 16:09:54 EDT 2017

STATUS

editing

approved

#13 by Ray Chandler at Mon Jun 26 16:09:43 EDT 2017

EXTENSIONS

a(20)=145 corrected by Philippe Guglielmetti, Dec 14 2016

a(43)=401 inserted by Michael Somos, Dec 21 2016

STATUS

approved

editing

#12 by Charles R Greathouse IV at Tue Feb 07 12:31:31 EST 2017

STATUS

editing

approved

#11 by Charles R Greathouse IV at Tue Feb 07 12:31:27 EST 2017

PROG

(PARI) v=vector(M=10^4); for(a=1, M, v[a] = []; fordiv(2*a, x, if(x<(y=2*a/x) && issquare(x^2+y^2, &z) && 1==gcd([x, y, z]), v[a] = concat(z, v[a])))); concat(v) /* Michael Somos, Dec 21 2016 */

STATUS

approved

editing

#10 by Michael Somos at Wed Dec 21 20:39:32 EST 2016

STATUS

editing

approved

#9 by Michael Somos at Wed Dec 21 20:37:28 EST 2016

DATA

5, 13, 17, 25, 41, 29, 37, 61, 65, 85, 53, 113, 65, 101, 145, 73, 85, 89, 181, 145, 221, 97, 125, 109, 197, 265, 149, 313, 257, 173, 137, 365, 185, 157, 325, 421, 229, 169, 481, 205, 185, 193, 401, 269, 545, 293

STATUS

approved

editing

Discussion

Wed Dec 21

20:39

Michael Somos: Added missing term for area = 7980 with 95^2 + 168^2 = 193^2 and 40^2 + 399^2 = 401^2 being the two Pythagorean triples.

#8 by Michael Somos at Wed Dec 21 20:33:09 EST 2016

STATUS

editing

approved

#7 by Michael Somos at Wed Dec 21 20:32:56 EST 2016

PROG

v=vector(M=10^4); for(a=1, M, v[a] = []; fordiv(2*a, x, if(x<(y=2*a/x) && issquare(x^2+y^2, &z) && 1==gcd([x, y, z]), v[a] = concat(z, v[a])))); concat(v) /* Michael Somos, Dec 21 2016 */

STATUS

proposed

editing

Discussion

Wed Dec 21

20:33

Michael Somos: Added more info.

#6 by Philippe Guglielmetti at Wed Dec 14 10:10:00 EST 2016

STATUS

editing

proposed

Discussion

Wed Dec 14

14:49

Michel Marcus: For this, the extension could be: a(20) corrected by

Wed Dec 21

16:10

Michel Marcus: Please add extension: a(20) corrected by

16:13

Michel Marcus: Do you have a program ?

#5 by Philippe Guglielmetti at Wed Dec 14 10:09:13 EST 2016

EXTENSIONS

corrected 20th term of the sequence, which is 145, not 142. the triple is (24, 143, 145), with area 1716, which is between 1710 (19, 180, 181) and 2310 (21, 220, 221). BTW there is no primitive triple with hypotenuse=142 (A020882)

Discussion

Wed Dec 14

10:09

Philippe Guglielmetti: corrected 20th term of the sequence, which is 145, not 142. the triple is (24, 143, 145), with area 1716, which is between 1710 (19, 180, 181) and 2310 (21, 220, 221). BTW there is no primitive triple with hypotenuse=142 (A020882)