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

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

Offset: 1

Author

Max Alekseyev, Nov 03 2009

Keywords

• nonn

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 */