A155921 -id:A155921 - cp's OEIS frontend

A154540 Decimal expansion of log_2 (15).

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			3.9068905956085185293240583734372066846246458007170616725105...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), this sequence, A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

RealDigits[Log[2, 15], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A154905 Decimal expansion of log_2 (18).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			4.1699250014423123629074778878956330175196288153849621209115...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), this sequence, A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

RealDigits[Log[2,18],10,120][[1]] (* Harvey P. Dale, Jul 12 2012 *)

Equals 1 + A020861 = 1 + 2*A020857. - Jianing Song, Nov 16 2024

A154995 Decimal expansion of log_2 (19).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			4.2479275134435854937935194229068344226935075696615340145815...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), this sequence, A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

RealDigits[Log[2, 19], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A155536 Decimal expansion of log_2 (21).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			4.3923174227787602888957082611796473174008410336586218441330...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), this sequence, A155693 (m=22), A155793 (m=23), A155921 (m=24).

RealDigits[Log[2, 21], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A155693 Decimal expansion of log_2 (22).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			4.4594316186372972561993630467257929587032315256817680713128...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), this sequence, A155793 (m=23), A155921 (m=24).

RealDigits[Log[2, 22], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

Equals 1 + A020863. - Jianing Song, Nov 16 2024

A155793 Decimal expansion of log_2 (23).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			4.5235619560570128722941482441626688444988251254425550594944...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), this sequence, A155921 (m=24).

RealDigits[Log[2, 23], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A229168 Define a sequence of real numbers by b(1)=2, b(n+1) = b(n) + log_2(b(n)); a(n) = smallest i such that b(i) >= 2^n.

Original entry on oeis.org

1, 3, 5, 7, 11, 17, 27, 44, 74, 127, 225, 402, 728, 1333, 2459, 4566, 8525, 15993, 30122, 56936, 107953, 205253, 391223, 747369, 1430648, 2743721, 5270959, 10141978, 19542806, 37708232, 72849931, 140905791, 272836175, 528832794, 1026008203, 1992390617

Offset: 1

N. J. A. Sloane, Sep 27 2013

nonn

			The initial terms of the b(n) sequence are approximately
2, 3.00000000000000000000000, 4.58496250072115618145375, 6.78187243514238888864578, 9.54355608312733448665509, 12.7980830210090262451102, 16.4759388461842196480290, 20.5182276175427023220954, 24.8770618274970204646817, 29.5138060245244394221195, 34.3971240984210783617324, ...
b(5) is the first term >= 8, so a(3) = 5.

Index entries for Colombian or self numbers and related sequences

Cf. A229169, A229170, A010062, A229167, A155921, A229177; also A004207, A229171, A229172, A229173.

# A229168, A229169, A229170.
Digits:=24;
log2:=evalf(log(2));
lis:=[2]; a:=2;
t1:=[1]; l:=2;
for i from 2 to 128 do
a:=evalf(a+log(a)/log2);
if a >= 2^l then
l:=l+1; t1:=[op(t1),i]; fi;
lis:=[op(lis),a];
od:
lis;
map(floor,lis);
map(ceil,lis);
t1;

n=1; p2=2^n; m=2; lg2=log(2); for(i=1, 1992390617, if(m>=p2, print(n " " i); n++; p2=2^n); m=m+log(m)/lg2) /* Donovan Johnson, Oct 04 2013 */

a(11)-a(36) from Donovan Johnson, Oct 04 2013

A229170 Define a sequence of real numbers by b(1)=2, b(n+1) = b(n) + log_2(b(n)); a(n) = ceiling( b(n) ).

Original entry on oeis.org

2, 3, 5, 7, 10, 13, 17, 21, 25, 30, 35, 40, 45, 51, 56, 62, 68, 74, 80, 87, 93, 100, 106, 113, 120, 127, 134, 141, 148, 155, 162, 170, 177, 185, 192, 200, 207, 215, 223, 231, 239, 246, 254, 262, 270, 278, 287, 295, 303, 311, 319, 328, 336, 345, 353, 361, 370, 378, 387, 396, 404, 413, 422, 430, 439, 448, 457, 465, 474

Offset: 1

N. J. A. Sloane, Sep 27 2013

nonn

			Comment from _N. J. A. Sloane_, Jun 07 2023: (Start)
b(1) to b(4) are:
  [2, 3, 3+ln(3)/ln(2), 3+ln(3)/ln(2)+ln(3+ln(3)/ln(2))/ln(2)]
b(1) to b(6) computed exactly and THEN converted to floating point are:
  2., 3., 4.58496250072115618145373894394, 6.78187243514238888864576363676, 9.54355608312733448665507868324, 12.7980830210090262451101642020. (End)

Index entries for Colombian or self numbers and related sequences

Cf. A229168, A229169, A155921, A229177.

Ceiling[NestList[N[#+Log2[#],1000]&,2,70]] (* Caution: this program uses an arbitrary cut-off at 1000 digits precision. - N. J. A. Sloane, Jun 07 2023 *) (* Harvey P. Dale, Jun 10 2023 *)

A229169 Define a sequence of real numbers by b(1)=2, b(n+1) = b(n) + log_2(b(n)); a(n) = floor( b(n) ).

Original entry on oeis.org

2, 3, 4, 6, 9, 12, 16, 20, 24, 29, 34, 39, 44, 50, 55, 61, 67, 73, 79, 86, 92, 99, 105, 112, 119, 126, 133, 140, 147, 154, 161, 169, 176, 184, 191, 199, 206, 214, 222, 230, 238, 245, 253, 261, 269, 277, 286, 294, 302, 310, 318, 327, 335, 344, 352, 360, 369, 377, 386, 395, 403, 412, 421, 429, 438, 447, 456, 464, 473, 482

Offset: 1

N. J. A. Sloane, Sep 27 2013

nonn

Index entries for Colombian or self numbers and related sequences

Cf. A229168, A229170, A155921, A229177.

A229177 Decimal expansion of 3 + log_2(3) + log_2(3 + log_2(3)).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Sep 28 2013

This is the fourth term in the sequence of real numbers discussed in A229168-A229170.

			6.7818724351423888886457636367782053029041818834546993272707...

Index entries for Colombian or self numbers and related sequences.

Cf. A229168, A229169, A229170, A155921, A020857.

RealDigits[3 + Log2[3] + Log2[3 + Log2[3]], 10, 120][[1]] (* Amiram Eldar, Jun 06 2023 *)

cp's OEIS Frontend

A154540 Decimal expansion of log_2 (15).

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A154905 Decimal expansion of log_2 (18).

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A154995 Decimal expansion of log_2 (19).

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A155536 Decimal expansion of log_2 (21).

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A155693 Decimal expansion of log_2 (22).

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A155793 Decimal expansion of log_2 (23).

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A229168 Define a sequence of real numbers by b(1)=2, b(n+1) = b(n) + log_2(b(n)); a(n) = smallest i such that b(i) >= 2^n.

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A229170 Define a sequence of real numbers by b(1)=2, b(n+1) = b(n) + log_2(b(n)); a(n) = ceiling( b(n) ).

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Mathematica

A229169 Define a sequence of real numbers by b(1)=2, b(n+1) = b(n) + log_2(b(n)); a(n) = floor( b(n) ).

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