Benedikt Otten - cp's OEIS frontend

User: Benedikt Otten

Benedikt Otten has authored 2 sequences.

A217313 Numbers for which there exist a base in which n contains more 1's than in binary.

4, 8, 16, 32, 40, 64, 112, 128, 129, 130, 148, 256, 257, 258, 259, 260, 274, 280, 292, 328, 336, 337, 352, 364, 388, 392, 400, 448, 512, 580, 608, 656, 768, 769, 770, 772, 776, 784, 832, 850, 1024, 1025, 1026, 1030, 1032, 1036, 1040, 1042, 1048, 1056, 1057, 1058, 1060, 1064, 1065

Offset: 1

Benedikt Otten, Mar 17 2013

Numbers n for which A062843(n) != A000120(n).

Every number of the form 2^m with m > 1 is included in the list.

			40 is 111 (3 ones) in base 3 and 101000 (2 ones) in base 2, therefore it is in the sequence.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Select[Table[n, {n, 1, 1000}], Max[Table[Count[IntegerDigits[#, b], 1], {b, 2, # + 1}]] != Count[IntegerDigits[#, 2], 1] &]

ones(n, b)=my(s); while(n, if(n%b==1, s++); n\=b); s
is(n)=if(n<4, return(0)); my(m=hammingweight(n), b=2); while(b++^(m-1)m,return(1))); 0 \\ Charles R Greathouse IV, Mar 19 2013

A218583 Decimal expansion of the limit of the n-fold application of the natural logarithm to A049384 as n tends to infinity.

Original entry on oeis.org

0, 6, 1, 3, 3, 1, 2, 4, 2, 3, 0, 0, 0, 8, 3, 5, 1, 2, 3, 4, 3, 9, 8, 5, 5, 9, 9, 6, 9, 5, 0, 0, 6, 0, 4, 5, 0, 6, 1, 2, 1, 0, 2, 6, 4, 5, 2, 8, 7, 7, 9, 7, 3, 3, 6, 4, 2, 5, 7, 5, 2, 0, 6, 6, 3, 4, 7, 8, 1, 6, 6, 9, 5, 6, 2, 0, 2, 8, 9, 4, 7, 0, 1, 6, 5, 1, 8, 3, 8, 9, 2, 5, 7, 9, 7, 4, 4, 8, 2

Offset: 0

Benedikt Otten, Nov 03 2012

The value can be calculated to an accuracy of at least 4.8*10^183230 decimal digits by calculating log(...log(7^...^1)...).

			-0.0613312423000835123439855996950060450612102645287...

Proof that the series converges (StackExchange, 10/09/2012)

Cf. A049384.

p[n_] := HoldForm[n]^(p[n - 1]); p[1] := 1; rules = {Log[x_ y_] :> Log[x] + Log[y], Log[x_^k_] :> k Log[x]}; lnn[x_, n_] := Log[lnn[x, n - 1]]; lnn[x_, 0] := x; RealDigits[ReleaseHold[lnn[p[7], 7] //. rules], 10, 100, 0]

Equals -log(...log(n^(n-1)^...^1)...) (n nested log).

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User: Benedikt Otten

A217313 Numbers for which there exist a base in which n contains more 1's than in binary.

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