A207384 A206815(n+1)-A206815(n).
1, 3, 2, 2, 2, 3, 1, 2, 2, 3, 1, 3, 2, 2, 1, 3, 2, 3, 1, 2, 2, 3, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 3, 2, 1, 2, 3, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 1, 2, 3, 2, 2, 1, 3, 2, 3, 2, 1, 2, 2, 2, 3, 2, 1, 2, 3, 2, 2, 1, 2, 2, 3, 2, 2, 1, 2, 2, 2, 2, 3, 1, 2, 2
Offset: 1
Keywords
Examples
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,..
Programs
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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 *)
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