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A258029 Numbers prime(k) such that D(prime(k), 3) = 0, where D( * , 3) = 3rd difference. 5

%I

%S 17,31,41,61,79,227,251,271,347,349,379,439,467,569,607,641,673,677,

%T 709,743,1031,1091,1277,1291,1427,1429,1487,1549,1607,1619,1657,1723,

%U 1741,1777,1861,1979,1987,2039,2131,2203,2371,2459,2477,2557,2677,2687,2689

%N Numbers prime(k) such that D(prime(k), 3) = 0, where D( * , 3) = 3rd difference.

%C Partition of the positive integers: A064149, A258027, A258028;

%C Corresponding partition of the primes: A258029, A258030, A258031.

%H Clark Kimberling, <a href="/A258029/b258029.txt">Table of n, a(n) for n = 1..1000</a>

%F D(prime(k), 3) = P(k+3) - 3*P(k+2) + 3*P(k+1) - P(k), where P(m) = prime(m) for m >= 1.

%t d = Differences[Table[Prime[n], {n, 1, 400}], 3];

%t u1 = Flatten[Position[d, 0]] (* A064149 *)

%t u2 = Flatten[Position[Sign[d], 1]] (* A258027 *)

%t u3 = Flatten[Position[Sign[d], -1]] (* A258028 *)

%t p1 = Prime[u1] (* A258029 *)

%t p2 = Prime[u2] (* A258030 *)

%t p3 = Prime[u3] (* A258031 *)

%Y Cf. A064149, A258027, A258028, A258030, A258031.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 05 2015

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Last modified August 12 17:17 EDT 2020. Contains 336439 sequences. (Running on oeis4.)