A154777
Numbers of the form x^2 + 2*y^2 with positive integers x and y.
Original entry on oeis.org
3, 6, 9, 11, 12, 17, 18, 19, 22, 24, 27, 33, 34, 36, 38, 41, 43, 44, 48, 51, 54, 57, 59, 66, 67, 68, 72, 73, 75, 76, 81, 82, 83, 86, 88, 89, 96, 97, 99, 102, 107, 108, 113, 114, 118, 121, 123, 129, 131, 132, 134, 136, 137, 139, 144, 146, 147, 150, 152, 153, 162, 163
Offset: 1
a(1) = 3 = 1^2 + 2*1^2 is the least number that can be written as A + 2B where A, B are positive squares.
a(2) = 6 = 2^2 + 2*1^2 is the second smallest number that can be written in this way.
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f[upto_]:=Module[{max=Ceiling[Sqrt[upto-1]]},Select[Union[ First[#]^2+ 2Last[#]^2&/@Tuples[Range[13],{2}]],#<=upto&]]; f[200] (* Harvey P. Dale, Jun 17 2011 *)
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isA154777(n,/* use optional 2nd arg to get other analogous sequences */c=2) = { for( b=1,sqrtint((n-1)\c), issquare(n-c*b^2) & return(1))}
for( n=1,200, isA154777(n) & print1(n","))
A339048
a(n) = 2*n^2 + 9.
Original entry on oeis.org
9, 11, 17, 27, 41, 59, 81, 107, 137, 171, 209, 251, 297, 347, 401, 459, 521, 587, 657, 731, 809, 891, 977, 1067, 1161, 1259, 1361, 1467, 1577, 1691, 1809, 1931, 2057, 2187, 2321, 2459, 2601, 2747, 2897, 3051, 3209, 3371, 3537, 3707, 3881
Offset: 0
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], ...
Showing 1-3 of 3 results.
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