A106321 - OEIS

%I #31 Jan 27 2017 13:32:20

%S 625,40000,455625

%N Smaller member of a Bhaskara pair (excluding Bhaskara twins, that is, include only a < b); a Bhaskara pair (a,b) is such that a^2 + b^2 = X^3 and a^3 + b^3 = Y^2.

%C Ordered by the larger of the pair. For corresponding larger value see A106322.

%C The sequence is infinite because it contains (as a subsequence) all numbers of the form a = 625*s^6 where s is a positive integer. The pairs are (a,b=2*a) =(625*s^6, 1250*s^6) associated with (X,Y) = (125*s^4, 46875*s^9). - _R. J. Mathar_, Jan 26 2017

%C The sequence also contains all numbers of the form a = 3430000*s^6 where s is a positive integer. The pairs are (a,b=3*a) associated with (X,Y) = (49000*s^4, 33614000000*s^9). The sequence also contains all numbers of the form a = 22936954625 *s^6 with b=4*a, all numbers of the form a = 19592846 *s^6 with b=5*a, all numbers of the form a = 19150763710393 *s^6 with b=6*a, all numbers of the form a= 3975350 *s^6 with b=7*a, all numbers of the form a = 3305810795625 * s^6 with b=8*a. - _R. J. Mathar_, Jan 26 2017

%D S. S. Gupta, 'Bhaskara Pairs' in 'Science Today' (subsequently renamed '2001') Jan 1988 pp. 68, Times of India, Mumbai.

%Y Cf. A106322, A106318, A106319, A106320.

%K hard,more,nonn,bref

%O 1,1

%A _Lekraj Beedassy_, Apr 29 2005

%E Corrected and extended _Jud McCranie_, Jul 04 2013