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A343809
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Divide the positive integers into subsets of lengths given by successive primes, then reverse the order of terms in each subset.
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3
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2, 1, 5, 4, 3, 10, 9, 8, 7, 6, 17, 16, 15, 14, 13, 12, 11, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59
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OFFSET
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1,1
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COMMENTS
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Irregular triangle read by rows T(n,k) in which row n lists the next p positive integers in decreasing order, where p is the n-th prime, with n >= 1.
The triangle has the following properties:
Column 1 gives the nonzero terms of A007504.
Column 4 gives the terms > 2 of A343859.
Column 5 gives the absolute values of the terms < -1 of A282329.
Column 6 gives the terms > 7 of A082548.
Column 7 gives the terms > 6 of A115030.
Records are in the column 1.
Indices of records are in the right border.
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LINKS
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FORMULA
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EXAMPLE
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Written as an irregular triangle in which row lengths give A000040 the sequence begins:
2, 1;
5, 4, 3;
10, 9, 8, 7, 6;
17, 16, 15, 14, 13, 12, 11;
28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18;
41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29;
58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42;
77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59;
...
(End)
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MAPLE
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R:= NULL: t:= 1:
for i from 1 to 20 do
p:= ithprime(i);
R:= R, seq(i, i=t+p-1..t, -1);
t:= t+p;
od:
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MATHEMATICA
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With[{nn=10}, Reverse/@TakeList[Range[Total[Prime[Range[nn]]]], Prime[Range[nn]]]]//Flatten (* Harvey P. Dale, Apr 27 2022 *)
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CROSSREFS
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Cf. A000027, A000040, A007504, A014284, A034956, A038722, A071148, A073612 (fixed points), A078423, A082548, A115030, A237589, A282329, A343859, A344891.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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