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A258036 Numbers k such that D(prime(k), k-1) < 0, where D( * , k-1) = (k-1)-st difference. 5

%I #5 Jun 05 2015 13:00:14

%S 4,6,8,10,12,14,17,19,21,23,25,28,30,32,34,36,38,41,43,45,47,48,50,52,

%T 54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,

%U 99,101,103,105,107,109,111,114,116,118,120,122,124,126,128

%N Numbers k such that D(prime(k), k-1) < 0, where D( * , k-1) = (k-1)-st difference.

%C Partition of the positive integers: A258036, A258037;

%C Corresponding partition of the primes: A258038, A258039.

%C Do all the terms of the difference sequence of A258036 belong to {1,2,3}?

%H Clark Kimberling, <a href="/A258036/b258036.txt">Table of n, a(n) for n = 1..1000</a>

%F D(prime(k), k-1) = sum{(-1)^i prime(k-i)*C(k-i),i); i = 0..k-1}

%e D(prime(2), 1) = 3 - 2 > 0;

%e D(prime(3), 2) = 5 - 2*3 + 2 > 0;

%e D(prime(4), 3) = 7 - 3*5 + 3*3 - 2 < 0, so a(1) = 4;

%t u = Table[Prime[Range[k]], {k, 1, 1000}];

%t v = Flatten[Table[Sign[Differences[u[[k]], k - 1]], {k, 1, 100}]];

%t w1 = Flatten[Position[v, -1]] (* A258036 *)

%t w2 = Flatten[Position[v, 1]] (* A258037 *)

%t Prime[w1] (* A258038 *)

%t Prime[w2] (* A258039 *)

%Y Cf. A258037, A258038, A258039.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 05 2015

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Last modified April 18 06:24 EDT 2024. Contains 371769 sequences. (Running on oeis4.)