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A057060
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a(n) = number of the row of (R(i,j)) that contains prime(n), where R(i,j) is the rectangle with descending antidiagonals 1; 2,3; 4,5,6; ...
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2
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1, 2, 2, 1, 1, 3, 2, 4, 2, 1, 3, 1, 5, 7, 2, 8, 4, 6, 1, 5, 7, 1, 5, 11, 6, 10, 12, 2, 4, 8, 7, 11, 1, 3, 13, 15, 4, 10, 14, 2, 8, 10, 1, 3, 7, 9, 1, 13, 17, 19, 2, 8, 10, 20, 4, 10, 16, 18, 1, 5, 7, 17, 7, 11, 13, 17, 6, 12, 22, 24, 2, 8, 16, 22, 1, 5, 11
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OFFSET
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1,2
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COMMENTS
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The rectangle has this corner:
1, 2, 4, 7, 11, 16, 22, 29, ...
3, 5, 8, 12, 17, 23, 30, 38, ...
6, 9, 13, 18, 24, 31, 39, 48, ...
10, 14, 19, 25, 32, 40, 49, 59, ...
15, 20, 26, 33, 41, 50, 60, 71, ...
21, 27, 34, 42, 51, 61, 72, 84, ...
28, 35, 43, 52, 62, 73, 85, 98, ...
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LINKS
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FORMULA
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EXAMPLE
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The 8th prime, 19, is in row 4, so a(8) = 4.
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MATHEMATICA
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s = Flatten[Table[Range[n], {n, 1, 40}]];
Table[s[[Prime[n]]], {n, 1, 100}]
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PROG
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(PARI) f(n) = n-binomial((sqrtint(8*n)+1)\2, 2); \\ A002260
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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