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A258036 Numbers k such that D(prime(k), k-1) < 0, where D( * , k-1) = (k-1)-st difference. 4
4, 6, 8, 10, 12, 14, 17, 19, 21, 23, 25, 28, 30, 32, 34, 36, 38, 41, 43, 45, 47, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 99, 101, 103, 105, 107, 109, 111, 114, 116, 118, 120, 122, 124, 126, 128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Partition of the positive integers:  A258036, A258037;

Corresponding partition of the primes: A258038, A258039.

Do all the terms of the difference sequence of A258036 belong to {1,2,3}?

LINKS

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

FORMULA

D(prime(k), k-1) = sum{(-1)^i prime(k-i)*C(k-i),i); i = 0..k-1}

EXAMPLE

D(prime(2), 1) = 3 - 2 > 0;

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

D(prime(4), 3) = 7 - 3*5 + 3*3 - 2 < 0, so a(1) = 4;

MATHEMATICA

u = Table[Prime[Range[k]], {k, 1, 1000}];

v = Flatten[Table[Sign[Differences[u[[k]], k - 1]], {k, 1, 100}]];

w1 = Flatten[Position[v, -1]] (* A258036 *)

w2 = Flatten[Position[v, 1]]  (* A258037 *)

Prime[w1]  (* A258038 *)

Prime[w2]  (* A258039 *)

CROSSREFS

Cf. A258037, A258038, A258039.

Sequence in context: A279040 A141109 A186331 * A242396 A061344 A066664

Adjacent sequences:  A258033 A258034 A258035 * A258037 A258038 A258039

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 05 2015

STATUS

approved

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Last modified March 25 19:30 EDT 2017. Contains 284082 sequences.