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A258029 Numbers prime(k) such that D(prime(k), 3) = 0, where D( * , 3) = 3rd difference. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 9 22:46 EDT 2020. Contains 335570 sequences. (Running on oeis4.)