|
|
A258039
|
|
Numbers prime(k) such that D(prime(k), k-1) > 0, where D( * , k-1) = (k-1)-st difference.
|
|
4
|
|
|
2, 3, 5, 11, 17, 23, 31, 41, 47, 53, 61, 71, 79, 89, 101, 103, 109, 127, 137, 149, 157, 167, 173, 181, 193, 199, 227, 233, 241, 257, 269, 277, 283, 307, 313, 331, 347, 353, 367, 379, 389, 401, 419, 431, 439, 449, 461, 467, 487, 499, 509, 541, 557, 569, 577
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
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, so a(1) = prime(1) = 2;
D(prime(3), 2) = 5 - 2*3 + 2 > 0, so a(2) = prime(2) = 3;
D(prime(4), 3) = 7 - 3*5 + 3*3 - 2 < 0.
|
|
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 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|