A106319 -id:A106319 - cp's OEIS frontend

A106318 Bhaskara twins: n such that 2n^2 = X^3 and 2n^3 = Y^2.

2, 128, 1458, 8192, 31250, 93312, 235298, 524288, 1062882, 2000000, 3543122, 5971968, 9653618, 15059072, 22781250, 33554432, 48275138, 68024448, 94091762, 128000000, 171532242, 226759808, 296071778, 382205952, 488281250, 617831552

Offset: 1

Lekraj Beedassy, Apr 29 2005

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Richard J. Mathar, Construction of Bhaskara Pairs, arXiv:1703.01677 [math.NT], 2017.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A106319, A106320, A106321, A106322.

Cf. A001014.

a106318 = (* 2) . (^ 6)  -- Reinhard Zumkeller, May 27 2015

LinearRecurrence[{7,-21,35,-35,21,-7,1},{2,128,1458,8192,31250,93312,235298},30] (* Harvey P. Dale, May 11 2017 *)

a(n)=2*n^6 \\ Charles R Greathouse IV, Feb 09 2012

a(n) = 2*n^6 = 2*A001014(n).
G.f.: 2*(1+x)*(1+56*x+246*x^2+56*x^3+x^4)/(1-x)^7. - Colin Barker, Apr 18 2012
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Wesley Ivan Hurt, Apr 23 2021

A106322 Larger member of a Bhaskara pair (excluding Bhaskara twins, i.e., include only a < b), sorted on the larger value; a Bhaskara pair (a,b) is such that a^2 + b^2 = X^3 and a^3 + b^3 = Y^2.

Original entry on oeis.org

1250, 80000, 911250

Offset: 1

Lekraj Beedassy, Apr 29 2005

This sequence does not miss any terms since it is sorted by the larger member of the pair. - Jud McCranie, Jul 05 2013

The sequence likely continues 5120000, 10290000, 19531250, 27827450, 52743945, 58320000, 75357100, ... - R. J. Mathar, Jan 27 2017

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

R. J. Mathar, Numerical Construction of Bhaskara Pairs
R. J. Mathar, Construction of Bhaskara Pairs, arXiv:1703.01677 [math.NT] (2017).

Cf. A106321, A106318, A106319, A106320.

A106320 SETMINUS A106318. - R. J. Mathar, Jan 27 2017

Corrected and extended by Jud McCranie, Jul 04 2013

A106320 Values b of a Bhaskara pair (a,b), a<=b, sorted on values of b. A Bhaskara pair (a,b) is such that a^2 + b^2 = X^3 and a^3 + b^3 = Y^2.

Original entry on oeis.org

2, 128, 1250, 1458, 8192, 31250, 80000, 93312, 235298, 524288, 911250, 1062882, 2000000

Offset: 1

Lekraj Beedassy, Apr 29 2005

For the corresponding values of a see A106319. This sequence is guaranteed to not be missing any terms. - Jud McCranie, Jul 04 2013

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

Richard J. Mathar, Construction of Bhaskara Pairs, arXiv:1703.01677 [math.NT], 2017.

Cf. A106319, A106318, A106320, A106321.

A106318 UNION A106322. - R. J. Mathar, Jan 27 2017

Corrected and extended by Jud McCranie, Jul 04 2013

A106321 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.

Original entry on oeis.org

625, 40000, 455625

Offset: 1

Lekraj Beedassy, Apr 29 2005

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

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

Cf. A106322, A106318, A106319, A106320.

Corrected and extended Jud McCranie, Jul 04 2013

cp's OEIS Frontend

A106318 Bhaskara twins: n such that 2*n^2 = X^3 and 2*n^3 = Y^2.

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A106322 Larger member of a Bhaskara pair (excluding Bhaskara twins, i.e., include only a < b), sorted on the larger value; a Bhaskara pair (a,b) is such that a^2 + b^2 = X^3 and a^3 + b^3 = Y^2.

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A106320 Values b of a Bhaskara pair (a,b), a<=b, sorted on values of b. A Bhaskara pair (a,b) is such that a^2 + b^2 = X^3 and a^3 + b^3 = Y^2.

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A106321 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.

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A106318 Bhaskara twins: n such that 2n^2 = X^3 and 2n^3 = Y^2.