A097268 -id:A097268 - cp's OEIS frontend

A155573 Intersection of A000404, A154777 and A092572: N = a^2 + b^2 = c^2 + 2d^2 = e^2 + 3f^2 for some positive integers a,b,c,d,e,f.

73, 97, 193, 241, 292, 313, 337, 388, 409, 433, 457, 577, 601, 657, 673, 769, 772, 873, 900, 937, 964, 1009, 1033, 1129, 1153, 1156, 1168, 1201, 1249, 1252, 1297, 1321, 1348, 1489, 1521, 1552, 1609, 1636, 1657, 1732, 1737, 1753, 1777, 1801, 1825, 1828

Offset: 1

M. F. Hasler, Jan 25 2009

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

isA155573(n,/* optional 2nd arg allows us to get other sequences */c=[3,2,1]) = { 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, isA155573(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

A155573 Intersection of A000404, A154777 and A092572: N = a^2 + b^2 = c^2 + 2d^2 = e^2 + 3f^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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PARI