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 A207385 A206818(n+1)-A206818(n). 2
 1, 2, 2, 2, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 3, 1, 2, 2, 1, 3, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 3, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 3, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequences A206815, A206818, A207384, A207835 illustrate the closeness of {j+pi(j)} to {k+(k+1)/log(k+1)}, as suggested by the prime number theorem and the conjecture that all the terms of A207384 and A207835 are in the set {1,2,3}. LINKS EXAMPLE The joint ranking is represented by 1 < 3 < 3.8 < 4.7 < 5 < 5.8 < 6 <7.1 < 8 < 8.3 < 9 < ... Positions of numbers j+pi(j): 1,2,5,7,9,... Positions of numbers k+(k+1)/log(k+1): 3,4,6,8,10,.. MATHEMATICA f[1, n_] := n + PrimePi[n]; f[2, n_] := n + N[(n + 1)/Log[n + 1]]; z = 500; t[k_] := Table[f[k, n], {n, 1, z}]; t = Sort[Union[t[1], t[2]]]; p[k_, n_] := Position[t, f[k, n]]; Flatten[Table[p[1, n], {n, 1, z}]]    (* A206815 *) Flatten[Table[p[2, n], {n, 1, z}]]    (* A206818 *) d1[n_] := p[1, n + 1] - p[1, n] Flatten[Table[d1[n], {n, 1, z - 1}]]  (* A207385 *) d2[n_] := p[2, n + 1] - p[2, n] Flatten[Table[d2[n], {n, 1, z - 1}]]  (* A207386 *) CROSSREFS Cf. A000720, A206815, A206818. Sequence in context: A306250 A145443 A192056 * A306242 A118144 A136691 Adjacent sequences:  A207382 A207383 A207384 * A207386 A207387 A207388 KEYWORD nonn AUTHOR Clark Kimberling, Feb 17 2012 STATUS approved

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Last modified June 25 07:53 EDT 2019. Contains 324347 sequences. (Running on oeis4.)