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 A258030 Numbers prime(k) such that D(prime(k), 3) > 0, where D( * , 3) = 3rd difference. 5
 3, 7, 13, 23, 37, 53, 67, 73, 89, 97, 103, 107, 113, 131, 139, 157, 173, 181, 193, 211, 223, 233, 241, 263, 277, 293, 307, 311, 317, 337, 359, 373, 389, 409, 421, 433, 449, 457, 461, 479, 491, 499, 509, 523, 547, 563, 577, 593, 613, 631, 653, 661, 691, 719 (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) = prime(2) = 3; 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) = prime(4) = 7; 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, A258028, A258029, A258031. Sequence in context: A103116 A303853 A075321 * A164787 A131205 A256309 Adjacent sequences:  A258027 A258028 A258029 * A258031 A258032 A258033 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 05 2015 STATUS approved

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Last modified July 29 15:22 EDT 2021. Contains 346346 sequences. (Running on oeis4.)