cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A155921 Decimal expansion of log_2(24) = 3+log_2(3).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Comments

This is the third term in the sequence of real numbers discussed in A229168-A229170. - N. J. A. Sloane, Sep 28 2013

Examples

			4.5849625007211561814537389439478165087598144076924810604557...

Links

Crossrefs

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), A155793 (m=23), this sequence.
Cf. A229177.

Programs

  • Mathematica
    RealDigits[Log[2,24],10,120][[1]] (* Harvey P. Dale, Dec 07 2011 *)

Formula

Equals 1 + A020864 = 2 + A020859 = 3 + A020857. - Jianing Song, Nov 16 2024

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

Views

Author

N. J. A. Sloane, Sep 27 2013

Keywords

Examples

			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.

Links

Crossrefs

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

Programs

  • Maple
    # 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;
  • PARI
    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 */

Extensions

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

A229171 Define a sequence of real numbers by b(1)=e, b(n+1) = b(n) + log(b(n)); a(n) = smallest i such that b(i) >= e^n.

Original entry on oeis.org

1, 5, 10, 20, 41, 86, 192, 441, 1039, 2493, 6072, 14960, 37199, 93193, 234957, 595562, 1516639, 3877905, 9950908, 25615654, 66127187, 171144672, 443966371, 1154115393, 3005950908
Offset: 1

Views

Author

N. J. A. Sloane, Sep 27 2013

Keywords

Examples

			The initial terms of the b(n) sequence are approximately
2.71828182845904523536029, 3.71828182845904523536029, 5.03154351597726806940929, 6.64727031503970856301384, 8.54147660649653209023621, 10.6864105040926911986276, 13.0553833920216929230460, 15.6245839611886549261305, 18.3734295299727029212384, 21.2843351036624388705641, 24.3423064646657059114213, 27.5345223079930416816192, 30.8499628820185220765989, ...
b(5) is the first term >= e^2, so a(2) = 5.

Links

Crossrefs

Cf. A229172, A229173, A229175; A229168, A229169, A229170, A010062, A229167; also A004207.

Programs

  • Maple
    # A229171, A229172, A229173.
Digits:=24;
e:=evalf(exp(1));
lis:=[e]; a:=e;
t1:=[1]; l:=2;
for i from 2 to 128 do
a:=evalf(a+log(a));
if a >= e^l then
l:=l+1; t1:=[op(t1),i]; fi;
lis:=[op(lis),a];
od:
lis;
map(floor,lis);
map(ceil,lis);
t1;
  • PARI
    n=1; m=exp(1); mn=m^n; for(i=1, 3005950908, if(m>=mn, print(n " " i); n++; mn=exp(1)^n); m=m+log(m)) /* Donovan Johnson, Oct 04 2013 */

Extensions

a(7)-a(25) from Donovan Johnson, Oct 04 2013

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

Views

Author

N. J. A. Sloane, Sep 27 2013

Keywords

Links

Crossrefs

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

Views

Author

N. J. A. Sloane, Sep 28 2013

Keywords

Comments

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

Examples

			6.7818724351423888886457636367782053029041818834546993272707...

Links

Crossrefs

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

Programs

  • Mathematica
    RealDigits[3 + Log2[3] + Log2[3 + Log2[3]], 10, 120][[1]] (* Amiram Eldar, Jun 06 2023 *)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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