A175406 -id:A175406 - cp's OEIS frontend

A319424 Records in A175046 (but written in base 2).

11, 1100, 11000, 110011, 1100011, 11001100, 110001100, 110011000, 1100110011, 11000110011, 11001100011, 110011001100, 1100011001100, 1100110001100, 1100110011000, 11001100110011, 110001100110011, 110011000110011, 110011001100011, 1100110011001100, 11000110011001100, 11001100011001100, 11001100110001100, 11001100110011000, 110011001100110011, 1100011001100110011

Offset: 1

N. J. A. Sloane, Sep 23 2018

More terms than usual are given in order to display the pattern.
Conjecture. a(n) is either an alternating string of 11's and 00's, or exactly one of the 00's is replaced by 000.
Conjecture is true (see A319423). - Chai Wah Wu, Oct 04 2018

Chai Wah Wu, Table of n, a(n) for n = 1..10099
N. J. A. Sloane, Transforms
Chai Wah Wu, Record values in appending and prepending bitstrings to runs of binary digits, arXiv:1810.02293 [math.NT], 2018

Cf. A175406, A319422, A319423.

A175407 a(n) = the least integer k such that (1+1/n)^k >= 3.

Original entry on oeis.org

2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75

Offset: 1

Zak Seidov, May 01 2010

nonn

Sequence of first differences consists just of 1's and 2's, no two consecutive 2's.

a(n)-A175406(n) may be arbitrarily large.

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Cf. A175406.

Mathematica
```
Table[Ceiling[Log[(1+1/n),3]],{n,200}]
```

Terms corrected by Jon E. Schoenfield, Apr 23 2014

cp's OEIS Frontend

A319424 Records in A175046 (but written in base 2).

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