A174885
Prime hypotenuses c with concatenation p = c//a//b a prime number.
Original entry on oeis.org
29, 409, 461, 661, 929, 1249, 1289, 1381, 1801, 1901, 2081, 2609, 2621, 2749, 3041, 3301, 3881, 5309, 5701, 6421, 6481, 6521, 6529, 7349, 7489, 7789, 8641, 8849, 9349, 9629, 9649, 9689, 9829, 10321, 10709, 10861, 12841, 14321, 14561, 15061, 16661
Offset: 1
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 01 2010
p = c//a//b: 292021, 409120391, 461380261, 661300589, 929920129, 1249960799, 12895601161,
13811020931, 18011680649, 19011820549, 208116401281, 260918801809, 262111002379,
27492580949, 30414403009, 330129401501, 388123603081, 53095300309, 570122205251
29^2=20^2+21^2, 409^2=120^2+391^2, 461^2=380^2+261^2,
661^2=300^2+589^2, 929^2=920^2+129^2, 1249^2=960^2+799^2,
1289^2=560^2+1161^2,1381^2=1020^2+931^2, 1801^2=1680^2+649^2,
1901^2=1820^2+549^2, 2081^2=1640^2+1281^2, 2609^2=1880^2+1809^2,
2621^2=1100^2+2379^2, 2749^2=2580^2+949^2, 3041^2=440^2+3009^2,
3301^2=2940^2+1501^2, 3881^2=2360^2+3081^2, 5309^2=5300^2+309^2,
5701^2=2220^2+5251^2
- W. W. R. Ball, H. S. M. Coxeter: Mathematical Recreations and Essays, New York: Dover, 1987
- L. E. Dickson: "Rational Right Triangles", ch. 4 in History of the Theory of numbers, vol. II, Dover Publications 2005
- W. Sierpinski: Pythagorean Triangles, Mineola, NY, Dover Publications, Inc, 2003
A307894
Hypotenuses of primitive Pythagorean triangles with prime length, having the property that the sum and absolute difference of the shorter legs are both prime numbers.
Original entry on oeis.org
13, 17, 37, 53, 73, 97, 109, 113, 137, 149, 193, 197, 233, 277, 317, 337, 401, 449, 457, 541, 613, 641, 653, 673, 709, 757, 809, 821, 877, 1009, 1061, 1093, 1117, 1129, 1201, 1289, 1297, 1381, 1481, 1549, 1733, 1873, 1877, 1913, 1933, 1997, 2017, 2053, 2153, 2213, 2221, 2377, 2417, 2437, 2557, 2797
Offset: 1
13 is a term because 12 + 5 = 17 and 12 - 5 = 7.
17 is a term because 15 + 8 = 23 and 15 - 8 = 7.
37 is a term because 35 + 12 = 47 and 35 - 12 = 23.
A308341
Hypotenuses of primitive Pythagorean triangles two sides of which are Pythagorean primes.
Original entry on oeis.org
13, 421, 1861, 5101, 16381, 60901, 83641, 100801, 106261, 135721, 161881, 205441, 218461, 337021, 388081, 431521, 571381, 637321, 697381, 926161, 1108561, 1460341, 1515541, 1806901, 1899301, 2334961, 2574181, 2601481, 2740141, 2834581, 2853661, 3248701, 3403441, 3723721, 3889261, 4503001
Offset: 1
13 is a term because 13 and 5 are Pythagorean primes and are sides of {5,12,13}.
421 is a term because 421 and 29 are Pythagorean primes and are sides of {29,420,421}.
1861 is a term because 1861 and 61 are Pythagorean primes and are sides of {61,1860,1861}.
5101 is a term because 5101 and 101 are Pythagorean primes and are sides of {101,5100,5101}.
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hyp(n) = {return((2*((n-1)/2)^2) + (2*((n-1)/2)) + 1);}
lista(n) = forprime(p=2, n, if((p%4 == 1) && isprime(p) && isprime(hyp(p)), print1(hyp(p), ", ")));
lista(3100)
A360280
Squares that are the hypotenuse of a primitive Pythagorean triangle.
Original entry on oeis.org
25, 169, 289, 625, 841, 1369, 1681, 2809, 3721, 4225, 5329, 7225, 7921, 9409, 10201, 11881, 12769, 15625, 18769, 21025, 22201, 24649, 28561, 29929, 32761, 34225, 37249, 38809, 42025, 48841, 52441, 54289, 58081, 66049, 70225, 72361, 76729, 78961, 83521, 85849, 93025, 97969
Offset: 1
169 is a term because 169 = 13^2 and (119,120,169) is a primitive Pythagorean triangle.
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