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A258029
Numbers prime(k) such that D(prime(k), 3) = 0, where D( * , 3) = 3rd difference.
5
17, 31, 41, 61, 79, 227, 251, 271, 347, 349, 379, 439, 467, 569, 607, 641, 673, 677, 709, 743, 1031, 1091, 1277, 1291, 1427, 1429, 1487, 1549, 1607, 1619, 1657, 1723, 1741, 1777, 1861, 1979, 1987, 2039, 2131, 2203, 2371, 2459, 2477, 2557, 2677, 2687, 2689
OFFSET
1,1
COMMENTS
Partition of the positive integers: A064149, A258027, A258028;
Corresponding partition of the primes: A258029, A258030, A258031.
LINKS
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.
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 05 2015
STATUS
approved