A227586 Numbers which occur exactly once in row 1 of the array at A227581.

1, 5, 16, 26, 36, 46, 56, 66, 76, 86, 96, 106, 116, 126, 136, 146, 156, 166, 176, 186, 196, 206, 216, 226, 236, 246, 257, 267, 277, 287, 297, 307, 317, 327, 337, 347, 357, 367, 377, 387, 397, 407, 417, 427, 437, 447, 457, 467, 477, 487, 497, 508, 518, 528

Offset

1,2

Comments

It appears that every positive integer k occurs exactly once or exactly twice as a solution of H(n) - H(n+k) < g-1 < H(n) - H(n+k-1) as n runs through the positive integers, where H denotes harmonic number, and g denotes the Euler-Mascheroni constant. See A227581.

Links

Clark Kimberling, Table of n, a(n) for n = 1..400

Example

That 5 occurs just once, and 4 and 6 each occur twice, corresponds to these inequalities:
H(6)  - H(6 + 4)  < g-1 < H(6)  - H(6 + 3),
H(7)  - H(7 + 4)  < g-1 < H(7)  - H(7 + 3),
H(8)  - H(8 + 5)  < g-1 < H(8)  - H(8 + 4),
H(9)  - H(9 + 6)  < g-1 < H(9)  - H(9 + 5),
H(10) - H(10 + 6) < g-1 < H(10) - H(10 + 5).

Mathematica

z = 1500; r[n_] := r[n] = Module[{Nn = N[n, 50]}, NestWhile[# + 1 &, Floor[(1 + n)/2], !       HarmonicNumber[1] + HarmonicNumber[Nn] - HarmonicNumber[Nn + #] < EulerGamma &]]; u[k_] := Length[Split[Table[r[n], {n, z}]][[k]]]; t = Table[u[k], {k, 1, z/2}]; Flatten[Position[t, 1]]  (* A227586 *)

Crossrefs

Cf. A227581.

Sequence in context: A274356 A275178 A171787 * A335416 A018197 A061874

Adjacent sequences: A227583 A227584 A227585 * A227587 A227588 A227589

Keyword

nonn,easy

Author

Clark Kimberling, Jul 17 2013

Status

approved