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A258031 Numbers prime(k) such that D(prime(k), 3) < 0, where D( * , 3) = 3rd difference. 5
2, 5, 11, 19, 29, 43, 47, 59, 71, 83, 101, 109, 127, 137, 149, 151, 163, 167, 179, 191, 197, 199, 229, 239, 257, 269, 281, 283, 313, 331, 353, 367, 383, 397, 401, 419, 431, 443, 463, 487, 503, 521, 541, 557, 571, 587, 599, 601, 617, 619, 643, 647, 659, 683 (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.

EXAMPLE

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

D(prime(2), 3) = 11 - 3*7 + 3*5 - 3 > 0;

D(prime(3), 3) = 13 - 3*11 + 3*7 - 5 < 0, so a(2) = prime(3) = 5;

D(prime(4), 3) = 17 - 3*13 + 3*11 - 7 > 0

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, A258029, A258030.

Sequence in context: A245207 A215762 A085626 * A290164 A160536 A024979

Adjacent sequences:  A258028 A258029 A258030 * A258032 A258033 A258034

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 05 2015

STATUS

approved

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Last modified August 9 05:12 EDT 2020. Contains 336319 sequences. (Running on oeis4.)