A003619 Not of form [ e^m ], m >= 1.

1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

Comments

If 1 is excluded (of form [e^0]) then complement of A000149. - Michel Marcus, Jun 16 2013

References

• J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 11.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• J. Lambek and L. Moser, Inverse and complementary sequences of natural numbers, Amer. Math. Monthly, 61 (1954), 454-458.

Crossrefs

Cf. A000195.

Programs

Haskell

a003619 n = n + floor (log (x + fromIntegral (floor $ log x)))
            where x = fromIntegral n + 1
-- Reinhard Zumkeller, Mar 17 2015

Mathematica

Table[n + Floor@ Log[n + 1 + Floor@ Log[n + 1]], {n, 50}] (* Michael De Vlieger, Oct 06 2017 *)

PARI

a(n) = n + floor( log (n + 1 + floor( log (n + 1) )) ) \\ Michel Marcus, Jun 16 2013

Formula

a(n) = n + [ log (n + 1 + [ log (n + 1) ]) ].