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A258027 Numbers k such that D(prime(k), 3) < 0, where D( * , 3) = 3rd difference. 5
2, 4, 6, 9, 12, 16, 19, 21, 24, 25, 27, 28, 30, 32, 34, 37, 40, 42, 44, 47, 48, 51, 53, 56, 59, 62, 63, 64, 66, 68, 72, 74, 77, 80, 82, 84, 87, 88, 89, 92, 94, 95, 97, 99, 101, 103, 106, 108, 112, 115, 119, 121, 125, 128, 130, 133, 135, 137, 139, 141, 143 (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;

D(prime(2), 3) = 11 - 3*7 + 3*5 - 3 > 0, so a(1) = 2;

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

D(prime(4), 3) = 17 - 3*13 + 3*11 - 7 > 0, so a(2) = 4.

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, A258028, A258029, A258030, A258031.

Sequence in context: A135146 A256956 A257637 * A053096 A155752 A145801

Adjacent sequences:  A258024 A258025 A258026 * A258028 A258029 A258030

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 05 2015

STATUS

approved

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Last modified August 9 14:23 EDT 2020. Contains 336323 sequences. (Running on oeis4.)