A106321 -id:A106321 - 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

A106319 Values a of a Bhaskara pair (a,b), a<=b, sorted by value 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, 625, 1458, 8192, 31250, 40000, 93312, 235298, 524288, 455625, 1062882, 2000000

Offset: 1

Lekraj Beedassy, Apr 29 2005

Contains Bhaskara twins (A106318). For corresponding values of b see A106320.

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. A106320, A106322. Non-sorted union of A106318 and A106321.

Corrected and extended by 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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A106319 Values a of a Bhaskara pair (a,b), a<=b, sorted by value 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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A106318 Bhaskara twins: n such that 2n^2 = X^3 and 2n^3 = Y^2.