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

1,1

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

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

Links

Table of n, a(n) for n=1..41.

Example

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

Crossrefs

A008846, A020882, A048161, A067756, A138044, A174825

Sequence in context: A010945 A022624 A042630 * A264160 A210302 A163021

Adjacent sequences: A174882 A174883 A174884 * A174886 A174887 A174888

Keyword

base,nonn,uned

Author

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

Extensions

More terms from Zak Seidov, Apr 04 2010

Status

approved