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

17, 31, 41, 61, 79, 227, 251, 271, 347, 349, 379, 439, 467, 569, 607, 641, 673, 677, 709, 743, 1031, 1091, 1277, 1291, 1427, 1429, 1487, 1549, 1607, 1619, 1657, 1723, 1741, 1777, 1861, 1979, 1987, 2039, 2131, 2203, 2371, 2459, 2477, 2557, 2677, 2687, 2689

Offset

1,1

Comments

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

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

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Formula

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.

Mathematica

d = Differences[Table[Prime[n], {n, 1, 400}], 3];
u1 = Flatten[Position[d, 0]]  (* A064149 *)
u2 = Flatten[Position[Sign[d], 1]]   (* A258027 *)
u3 = Flatten[Position[Sign[d], -1]]  (* A258028 *)
p1 = Prime[u1] (* A258029 *)
p2 = Prime[u2] (* A258030 *)
p3 = Prime[u3] (* A258031 *)

Crossrefs

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

Sequence in context: A172287 A062579 A134076 * A321596 A160961 A260805

Adjacent sequences: A258026 A258027 A258028 * A258030 A258031 A258032

Keyword

nonn,easy

Author

Clark Kimberling, Jun 05 2015

Status

approved