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Search: id:A083362
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| A083362 |
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Square table, read by antidiagonals, of least distinct positive integers such that the sum of any two consecutive terms in any row is a square number. |
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+0
3
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| 1, 3, 2, 6, 7, 4, 10, 9, 5, 8, 15, 16, 11, 17, 12, 21, 20, 14, 19, 13, 18, 28, 29, 22, 30, 23, 31, 24, 36, 35, 27, 34, 26, 33, 25, 32, 45, 46, 37, 47, 38, 48, 39, 49, 40, 55, 54, 44, 53, 43, 52, 42, 51, 41, 50, 66, 67, 56, 68, 57, 69, 58, 70, 59, 71, 60, 78, 77, 65, 76, 64, 75
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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A permutation of the natural numbers.
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FORMULA
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T(0, k)=(k+1)*(k+2)/2 for k>=0, T(n, 0)=floor((n+1)^2/2) for n>0, T(n, k+1)=(2*floor((n+1)/2) + k+1)^2 - T(n, k) for n>0 and k>=0.
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EXAMPLE
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Table begins:
1 3 6 10 15 21 28 36 45 55 66 ...
2 7 9 16 20 29 35 46 54 67 77 ...
4 5 11 14 22 27 37 44 56 65 79 ...
8 17 19 30 34 47 53 68 76 93 103 ...
12 13 23 26 38 43 57 64 80 89 107 ...
18 31 33 48 52 69 75 94 102 123 133 ...
24 25 39 42 58 63 81 88 108 117 139 ...
32 49 51 70 74 95 101 124 132 157 167 ...
40 41 59 62 82 87 109 116 140 149 175 ...
50 71 73 96 100 125 131 158 166 195 205 ...
60 61 83 86 110 115 141 148 176 185 215 ...
72 97 99 126 130 159 165 196 204 237 247 ...
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CROSSREFS
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Cf. A083363 (diagonal), A083364 (anti-diagonal sums).
Sequence in context: A154445 A165199 A120231 this_sequence A153142 A154447 A003188
Adjacent sequences: A083359 A083360 A083361 this_sequence A083363 A083364 A083365
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KEYWORD
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nonn,tabl,nice
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 27 2003
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