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A227586 Numbers which occur exactly once in row 1 of the array at A227581. 2
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 (list; graph; refs; listen; history; text; internal format)
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 goes 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]]  (* A277586 *)

CROSSREFS

Cf. A227581.

Sequence in context: A274356 A275178 A171787 * A018197 A061874 A017449

Adjacent sequences:  A227583 A227584 A227585 * A227587 A227588 A227589

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 17 2013

STATUS

approved

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Last modified January 23 01:55 EST 2018. Contains 298093 sequences.