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 A258037 Numbers k such that D(prime(k), k-1) > 0, where D( * , k-1) = (k-1)-st difference. 5
 1, 2, 3, 5, 7, 9, 11, 13, 15, 16, 18, 20, 22, 24, 26, 27, 29, 31, 33, 35, 37, 39, 40, 42, 44, 46, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 100, 102, 104, 106, 108, 110, 112, 113, 115, 117, 119, 121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Partition of the positive integers: A258036, A258037; Corresponding partition of the primes: A258038, A258039. Conjecture: all the terms of the difference sequence of A258037 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, so a(1) = 1; D(prime(3), 2) = 5 - 2*3 + 2 > 0, so a(2) = 2; 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 *) p1 = Prime[w1] (* A258038 *) p2 = Prime[w2] (* A258039 *) CROSSREFS Cf. A258036, A258038, A258039. Sequence in context: A066935 A042943 A306466 * A186330 A153809 A355330 Adjacent sequences: A258034 A258035 A258036 * A258038 A258039 A258040 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 05 2015 STATUS approved

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Last modified April 16 17:36 EDT 2024. Contains 371749 sequences. (Running on oeis4.)