A092572 -id:A092572 - cp's OEIS frontend

A158937 Numbers of the form x^2+3y^2 where x and y are positive integers (with repetitions).

4, 7, 12, 13, 16, 19, 21, 28, 28, 28, 31, 36, 37, 39, 43, 48, 49, 52, 52, 52, 57, 61, 63, 64, 67, 73, 76, 76, 76, 79, 84, 84, 84, 91, 91, 93, 97, 100, 103, 108, 109, 111, 112, 112, 112, 117, 124, 124, 124, 127, 129, 133, 133, 139, 144, 147, 148, 148, 148, 151, 156, 156, 156, 157, 163, 169, 171, 172, 172, 172, 175, 181, 183, 189, 192, 193, 196, 196, 196, 196, 199, 201, 208, 208, 208, 211, 217, 217, 219, 223, 228, 228, 228, 229, 237, 241, 244, 244, 244, 247

Offset: 1

Zak Seidov, Mar 26 2011

nonn

Least integer m with exactly n repetitions, {m,n}: {4,1},{91,2},{28,3},{196,4},{31213,5},{364,6}, {9604,7},{53599,8},{2548,9},{470596,10}.

This is an important quadratic form with a small determinant, so a list of its values with repetition is of interest. - N. J. A. Sloane, Apr 02 2011

			m=28: {x,y}={5,1},{4,2},{1,3}.

Cf. A092572 Numbers of the form x^2+3y^2 where x and y are positive integers.

A155572 Intersection of A000404, A154777 and A154778: N = a^2 + b^2 = c^2 + 2d^2 = e^2 + 5f^2 for some positive integers a,b,c,d,e,f.

Original entry on oeis.org

41, 89, 164, 225, 241, 281, 356, 369, 401, 409, 449, 521, 569, 601, 641, 656, 761, 769, 801, 809, 881, 900, 929, 964, 1009, 1025, 1049, 1124, 1129, 1201, 1249, 1289, 1321, 1361, 1409, 1424, 1476, 1481, 1489, 1521, 1601, 1604, 1609, 1636, 1681, 1721, 1796

Offset: 1

M. F. Hasler, Jan 25 2009

Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717, A155560-A155578.

isA155572(n,/* optional 2nd arg allows us to get other sequences */c=[5,2,1]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,1999, isA155572(n) & print1(n","))

A155711 Intersection of A154777 and A155717: N = a^2 + 2b^2 = c^2 + 7d^2 for some positive integers a,b,c,d.

Original entry on oeis.org

11, 43, 44, 67, 72, 88, 99, 107, 113, 121, 137, 144, 163, 172, 176, 179, 193, 211, 233, 268, 275, 281, 288, 331, 337, 344, 347, 352, 379, 387, 396, 401, 428, 443, 449, 452, 457, 473, 484, 491, 499, 536, 539, 547, 548, 569, 571, 576, 603, 617, 641, 648, 652

Offset: 1

M. F. Hasler, Jan 25 2009

Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717, A155560-A155578.

isA155711(n,/* optional 2nd arg allows us to get other sequences */c=[7,2]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,999, isA155711(n) & print1(n","))

A155713 Intersection of A154778 and A155716: N = a^2 + 5b^2 = c^2 + 6d^2 for some positive integers a,b,c,d.

Original entry on oeis.org

49, 70, 105, 145, 150, 166, 196, 214, 225, 241, 249, 280, 294, 321, 406, 409, 420, 441, 454, 505, 580, 600, 601, 609, 630, 664, 681, 694, 721, 726, 745, 769, 784, 841, 856, 870, 886, 889, 900, 934, 945, 964, 996, 1009, 1030, 1041, 1089, 1120, 1126, 1129

Offset: 1

M. F. Hasler, Jan 25 2009

Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717, A155560-A155578.

isA155713(n,/* optional 2nd arg allows us to get other sequences */c=[6,5]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,999, isA155713(n) & print1(n","))

cp's OEIS Frontend

A158937 Numbers of the form x^2+3y^2 where x and y are positive integers (with repetitions).

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A155572 Intersection of A000404, A154777 and A154778: N = a^2 + b^2 = c^2 + 2d^2 = e^2 + 5f^2 for some positive integers a,b,c,d,e,f.

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A155711 Intersection of A154777 and A155717: N = a^2 + 2b^2 = c^2 + 7d^2 for some positive integers a,b,c,d.

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A155713 Intersection of A154778 and A155716: N = a^2 + 5b^2 = c^2 + 6d^2 for some positive integers a,b,c,d.

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