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A258036
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Numbers k such that D(prime(k), k-1) < 0, where D( * , k-1) = (k-1)-st difference.
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5
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4, 6, 8, 10, 12, 14, 17, 19, 21, 23, 25, 28, 30, 32, 34, 36, 38, 41, 43, 45, 47, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 99, 101, 103, 105, 107, 109, 111, 114, 116, 118, 120, 122, 124, 126, 128
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OFFSET
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1,1
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COMMENTS
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Do all the terms of the difference sequence of A258036 belong to {1,2,3}?
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LINKS
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FORMULA
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D(prime(k), k-1) = sum{(-1)^i prime(k-i)*C(k-i),i); i = 0..k-1}
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EXAMPLE
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D(prime(2), 1) = 3 - 2 > 0;
D(prime(3), 2) = 5 - 2*3 + 2 > 0;
D(prime(4), 3) = 7 - 3*5 + 3*3 - 2 < 0, so a(1) = 4;
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MATHEMATICA
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u = Table[Prime[Range[k]], {k, 1, 1000}];
v = Flatten[Table[Sign[Differences[u[[k]], k - 1]], {k, 1, 100}]];
w1 = Flatten[Position[v, -1]] (* A258036 *)
w2 = Flatten[Position[v, 1]] (* A258037 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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