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Revision History for A006339

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A006339

Least hypotenuse of n distinct Pythagorean triangles.
(history; published version)

#30 by Joerg Arndt at Sat Aug 03 01:52:13 EDT 2024

STATUS

reviewed

approved

#29 by Michel Marcus at Sat Aug 03 01:08:14 EDT 2024

STATUS

proposed

reviewed

#28 by Hugo Pfoertner at Fri Aug 02 23:40:43 EDT 2024

STATUS

editing

proposed

#27 by Hugo Pfoertner at Fri Aug 02 23:40:04 EDT 2024

DATA

1, 5, 25, 125, 65, 3125, 15625, 325, 390625, 1953125, 1625, 48828125, 4225, 1105, 6103515625, 30517578125, 40625, 21125, 3814697265625, 203125, 95367431640625, 476837158203125, 5525, 11920928955078125, 274625, 5078125, 1490116119384765625, 528125, 25390625, 186264514923095703125

STATUS

approved

editing

Discussion

Fri Aug 02

23:40

Hugo Pfoertner: Usual length of DATA.

#26 by Jon E. Schoenfield at Sat Jan 11 23:12:23 EST 2020

STATUS

proposed

approved

#25 by Jon E. Schoenfield at Sat Jan 11 23:12:21 EST 2020

STATUS

editing

proposed

#24 by Jon E. Schoenfield at Sat Jan 11 23:12:18 EST 2020

LINKS

Ray Chandler, <a href="/A006339/b006339.txt">Table of n, a(n) for n = 0..1438</a> (a(1439) exceeds 1000 digits).

STATUS

approved

editing

#23 by Russ Cox at Fri Mar 30 18:35:06 EDT 2012

AUTHOR

_David W. Wilson (davidwwilson(AT)comcast.net)_

Discussion

Fri Mar 30

18:35

OEIS Server: https://oeis.org/edit/global/202

#22 by Ray Chandler at Sat Jan 07 10:20:16 EST 2012

STATUS

editing

approved

#21 by Ray Chandler at Sat Jan 07 09:54:11 EST 2012

MATHEMATICA

primeCon1Mod4 = Select[ Prime[ Range[ 50 ] ], (Mod[ #1, 4 ] == 1) & ]; (Times @@ (Take[ primeCon1Mod4, Length[ #1 ] ]^Reverse[ (#1 - 1)/2 ])) & /@ ((Join @@ (Table[ #1[ [ 1 ] ], {#1[ [ 2 ] ]} ] & /@ FactorInteger[ #1*2 + 1 ])) & /@ Range[ 0, 50 ]) (* Albert Mao, Dec 03 2006 *)

oneModFourPrimes[1] = 5;

oneModFourPrimes[n_] := oneModFourPrimes[n] = NestWhile[NextPrime, NextPrime[oneModFourPrimes[n - 1]], Mod[#, 4] != 1 & ];

factorizations[1, limit_] = {{}};

factorizations[n_, limit_] := factorizations[n, limit] = Join @@ Table[Prepend[#, d]& /@ factorizations[n/d, d], {d, Select[Rest[Divisors[n]], # <= limit & ]}];

leastHypotenuse[n_] := Min[(Times @@ (Array[oneModFourPrimes, Length[#]]^((# - 1)/2)) & ) /@ factorizations[2*n + 1, 2*n + 1]];

Array[leastHypotenuse, 30, 0]

(* Albert H. Mao, Jan 06 2012 *)

STATUS

approved

editing

Discussion

Sat Jan 07

10:20

Ray Chandler: Albert Mao replaced his Mma code from 2006 in response to example which produced incorrect results.