A004081 a(n) = n-th positive integer such that only one integer lies between exp(s(m)) and exp(s(m+1)), where s(m) = 1 + 1/2 + 1/3 + . . . + 1/m.

4, 8, 13, 17, 22, 26, 31, 36, 40, 45, 49, 54, 58, 63, 68, 72, 77, 81, 86, 90, 95, 99, 104, 109, 113, 118, 122, 127, 131, 136, 141, 145, 150, 154, 159, 163, 168, 173, 177, 182, 186, 191, 195, 200

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

Equivalently, this is a list of integers m for which there is exactly one integer k satisfying 1+1/2+...+1/m < log(k) < 1+1/2+...+1/(m+1). - Clark Kimberling May 30 2013.

Links

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

Programs

Mathematica

Flatten[Position[Differences[Table[Floor[E^Sum[1/k, {k, 1, m}]], {m, 1, 500}]], 1]] (* Clark Kimberling, May 30 2013 *)

PARI

lista(n) = {old = 1; expo = exp(old); for (i=2, n, new = old + 1/i; expn = exp(new); if (floor(expn)==ceil(expo), print1(i-1, ", ")); old = new; expo = expn;);} \\ Michel Marcus, Mar 21 2013

Formula

Conjecturally, a(n) = floor(n/(2 - exp(g)) - 1/2 + exp(g)/(24n)), where g is the Euler-Mascheroni constant. - David W. Cantrell (DWCantrell(AT)sigmaxi.net), Aug 11 2007