cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A166930 Positive integers m such that m^4 = a^2 + b^2 and a + b = c^2 for some positive coprime integers a, b, c.

Original entry on oeis.org

2165017, 15512114571284835412957, 368440923990671763222767414151367493861848396861, 29032470413228645503712143213832535500985227130245791625262982715784415755764157625
Offset: 1

Views

Author

Max Alekseyev, Oct 23 2009

Keywords

Comments

Square roots of the hypotenuses of Pythagorean triangles in which the hypotenuse and the sum of the legs are squares. In a letter to Mersenne in the year 1643, Fermat asserted that the smallest such triangle has the legs 4565486027761 and 1061652293520, and the hypotenuse a(1)^2 = 4687298610289.
Subsequence of A166929 which allows a,b be nonzero.
Values of m in coprime solutions to 2m^4 = c^4 + d^2 with d < c^2 (so that a,b = (c^2 +- d)/2). Corresponding values of c are given in A167438.

References

  • W. Sierpinski. Pythagorean Triangles. Dover Publications, 2003, ISBN 0-486-43278-5.

Links

Crossrefs

Cf. A166929, A167437, A167438.

Extensions

Edited by Max Alekseyev, Nov 03 2009

A167437 Positive integers c such that c^2 = a + b and a^2 + b^2 = m^4 for some coprime integers a, b, m.

Original entry on oeis.org

1, 1343, 2372159, 9788425919, 5705771236038721, 17999572487701067948161, 173658539553825212149513251457, 75727152767742719949099952561135816319, 437825148963391521638828389137484882137402791039
Offset: 1

Views

Author

Max Alekseyev, Nov 03 2009

Keywords

Comments

Corresponding values of m are given in A166929 - see it for further details.
Terms with positive a, b are given in A167438.
This is the absolute value of a bisection of a generalized Somos-5 sequence. - Michael Somos, Nov 04 2022

Programs

  • PARI
    {a(n) = local(x, v); n = abs(2*n+1); (x = m-> v[abs(m)+1]); v = vector(max(3, n+1), m, 1); v[3] = -3; for(k=3, n, v[k+1] = -(13*x(k-1)*x(k-4) + 42*x(k-2)*x(k-3)) / x(k-5)); abs(x(n))}; /* Michael Somos, Nov 04 2022 */
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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