A155561
Intersection of A000404 and A154777: N = a^2 + b^2 = c^2 + 2d^2 with a,b,c,d>0.
Original entry on oeis.org
17, 18, 34, 41, 68, 72, 73, 82, 89, 97, 113, 136, 137, 146, 153, 162, 164, 178, 193, 194, 225, 226, 233, 241, 242, 257, 272, 274, 281, 288, 289, 292, 306, 313, 328, 337, 353, 356, 369, 386, 388, 401, 409, 425, 433, 449, 450, 452, 457, 466, 482, 514, 521, 544
Offset: 1
a(1)=17 is the least number that can be written as A+B and C+2D where A,B,C,D are positive squares (namely 17 = 1^2 + 4^2 = 3^2 + 2*2^2).
a(2)=18 is the second smallest number which figures in A000404 and in A154777 as well.
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isA155561(n,/* use optional 2nd arg to get other analogous sequences */c=[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=1,10^3, isA155561(n) & print1(n","))
A339047
a(n) gives the multiplicity for A154777(n) representable as x^2 + 2*y^2 with positive integers x and y, for n >= 1.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3
Offset: 1
See A338432 for examples.
The pairs [A154777(n), a(n)] begin:
[3, 1], [6, 1], [9, 1], [11, 1], [12, 1], [17, 1], [18, 1], [19, 1], [22, 1], [24, 1], [27, 2], [33, 2], [34, 1], [36, 1], [38, 1], [41, 1], [43, 1], [44, 1], [48, 1], [51, 2], [54, 2], [57, 2], [59, 1], [66, 2], [67, 1], [68, 1], [72, 1], [73, 1], [75, 1], [76, 1], [81, 2], [82, 1], [83, 1], [86, 1], [88, 1], [89, 1], [96, 1], [97, 1], [99, 3], ...
A155574
Intersection of A154777 and A092572: N = a^2 + 2b^2 = c^2 + 3d^2 for some positive integers a,b,c,d.
Original entry on oeis.org
12, 19, 36, 43, 48, 57, 67, 73, 76, 97, 108, 129, 139, 144, 147, 163, 171, 172, 192, 193, 201, 211, 219, 228, 241, 268, 283, 291, 292, 300, 304, 307, 313, 324, 331, 337, 361, 379, 387, 388, 409, 417, 432, 433, 441, 457, 475, 484, 489, 499, 507, 513, 516, 523
Offset: 1
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isA155574(n,/* optional 2nd arg allows us to get other sequences */c=[3,2]) = { 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, isA155574(n) & print1(n","))
A155577
Intersection of A154777 and A154778: N = a^2 + 2b^2 = c^2 + 5d^2 for some positive integers a,b,c,d.
Original entry on oeis.org
6, 9, 24, 36, 41, 54, 81, 86, 89, 96, 129, 134, 144, 150, 164, 166, 201, 214, 216, 225, 241, 246, 249, 281, 294, 321, 324, 326, 344, 356, 369, 384, 401, 409, 441, 449, 454, 486, 489, 516, 521, 534, 536, 566, 569, 576, 600, 601, 614, 641, 656, 664, 681, 694
Offset: 1
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isA155577(n,/* optional 2nd arg allows us to get other sequences */c=[5,2]) = { 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, isA155577(n) & print1(n","))
A155709
Intersection of A154777 and A155716: N = a^2 + 2b^2 = c^2 + 6d^2 for some positive integers a,b,c,d.
Original entry on oeis.org
22, 33, 73, 88, 97, 118, 121, 132, 150, 166, 177, 193, 198, 214, 225, 241, 249, 262, 292, 294, 297, 313, 321, 337, 352, 358, 388, 393, 409, 433, 438, 441, 454, 457, 472, 484, 502, 528, 537, 550, 577, 582, 600, 601, 649, 657, 664, 673, 681, 694, 708, 726, 753
Offset: 1
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isA155709(n,/* optional 2nd arg allows us to get other sequences */c=[6,2]) = { 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, isA155709(n) & print1(n","))
A201592
Least value of x arising in A154777(n).
Original entry on oeis.org
1, 2, 1, 3, 2, 3, 4, 1, 2, 4, 3, 1, 4, 2, 6, 3, 5, 6, 4, 1, 2, 5, 3, 4, 7, 6, 8, 1, 5, 2, 3, 8, 9, 6, 4, 9, 8, 5, 1, 2, 3, 6, 9, 4, 10, 7, 5, 1, 9, 2, 6, 8, 3, 11, 4, 12, 7, 10, 12, 5, 8, 1, 6, 2, 3, 10, 12, 7, 4, 9, 5, 8, 11, 12, 6, 1, 2, 3, 7, 14, 4, 11
Offset: 1
A201593
Largest value of y arising in A154777(n).
Original entry on oeis.org
1, 1, 2, 1, 2, 2, 1, 3, 3, 2, 3, 4, 3, 4, 1, 4, 3, 2, 4, 5, 5, 4, 5, 5, 3, 4, 2, 6, 5, 6, 6, 3, 1, 5, 6, 2, 4, 6, 7, 7, 7, 6, 4, 7, 3, 6, 7, 8, 5, 8, 7, 6, 8, 3, 8, 1, 7, 5, 2, 8, 7, 9, 8, 9, 9, 6, 4, 8, 9, 7, 9, 8, 6, 5, 9, 10, 10, 10, 9, 3, 10, 7
Offset: 1
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
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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","))
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.
Original entry on oeis.org
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
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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
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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","))
Showing 1-10 of 36 results.
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