A174885 Prime hypotenuses c with concatenation p = c//a//b a prime number.

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

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 01 2010

Keywords

• base
• nonn
• uned

Comments

See comments in A174825

c is the prime hypotenuse c, i. e. c of a primitive Pythagorean triple: a^2 + b^2 = c^2

Examples

			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
		

References

• 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

Crossrefs

A008846, A020882, A048161, A067756, A138044, A174825

Extensions

More terms from Zak Seidov, Apr 04 2010