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 A258036 Numbers k such that D(prime(k), k-1) < 0, where D( * , k-1) = (k-1)-st difference. 5
 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: A333197 A289426 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 February 28 04:16 EST 2024. Contains 370379 sequences. (Running on oeis4.)