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A258028 Numbers k such that D(prime(k), 3) > 0, where D( * , 3) = 3rd difference. 5
1, 3, 5, 8, 10, 14, 15, 17, 20, 23, 26, 29, 31, 33, 35, 36, 38, 39, 41, 43, 45, 46, 50, 52, 55, 57, 60, 61, 65, 67, 71, 73, 76, 78, 79, 81, 83, 86, 90, 93, 96, 98, 100, 102, 105, 107, 109, 110, 113, 114, 117, 118, 120, 124, 126, 129, 131, 134, 136, 138, 140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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) = 1;

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

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

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, A258029, A258030, A258031.

Sequence in context: A091309 A027922 A051611 * A005004 A006218 A062839

Adjacent sequences:  A258025 A258026 A258027 * A258029 A258030 A258031

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 05 2015

STATUS

approved

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Last modified August 14 09:14 EDT 2020. Contains 336480 sequences. (Running on oeis4.)