A199170 -id:A199170 - cp's OEIS frontend

A200338 Decimal expansion of least x > 0 satisfying x^2 + 1 = tan(x).

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

Offset: 1

Clark Kimberling, Nov 16 2011

For many choices of a,b,c, there is exactly one x satisfying a*x^2 + b*x + c = tan(x) and 0 < x < Pi/2.
Guide to related sequences, with graphs included in Mathematica programs:
a.... b.... c.... x
... 0.... 1.... A200338
... 0.... 2.... A200339
... 0.... 3.... A200340
... 0.... 4.... A200341
... 1.... 1.... A200342
... 1.... 2.... A200343
... 1.... 3.... A200344
... 1.... 4.... A200345
... 2.... 1.... A200346
... 2.... 2.... A200347
... 2.... 3.... A200348
... 2.... 4.... A200349
... 3.... 1.... A200350
... 3.... 2.... A200351
... 3.... 3.... A200352
... 3.... 4.... A200353
... 4.... 1.... A200354
... 4.... 2.... A200355
... 4.... 3.... A200356
... 4.... 4.... A200357
... 0.... 1.... A200358
... 0.... 3.... A200359
... 1.... 1.... A200360
... 1.... 2.... A200361
... 1.... 3.... A200362
... 1.... 4.... A200363
... 2.... 1.... A200364
... 2.... 3.... A200365
... 3.... 1.... A200366
... 3.... 2.... A200367
... 3.... 3.... A200368
... 3.... 4.... A200369
... 4.... 1.... A200382
... 4.... 3.... A200383
... 0.... 1.... A200384
... 0.... 2.... A200385
... 0.... 4.... A200386
... 1.... 1.... A200387
... 1.... 2.... A200388
... 1.... 3.... A200389
... 1.... 4.... A200390
... 2.... 1.... A200391
... 2.... 2.... A200392
... 2.... 3.... A200393
... 2.... 4.... A200394
... 3.... 1.... A200395
... 3.... 2.... A200396
... 3.... 4.... A200397
... 4.... 1.... A200398
... 4.... 2.... A200399
... 4.... 3.... A200400
... 4.... 4.... A200401
... 0.... 1.... A200410
... 0.... 3.... A200411
... 1.... 1.... A200412
... 1.... 2.... A200413
... 1.... 3.... A200414
... 1.... 4.... A200415
... 2.... 1.... A200416
... 2.... 3.... A200417
... 3.... 1.... A200418
... 3.... 2.... A200419
... 3.... 3.... A200420
... 3.... 4.... A200421
... 4.... 1.... A200422
... 4.... 3.... A200423
.. -1.... 1.... A200477
.. -1.... 2.... A200478
.. -1.... 3.... A200479
.. -1.... 4.... A200480
.. -2.... 1.... A200481
.. -2.... 2.... A200482
.. -2.... 3.... A200483
.. -2.... 4.... A200484
.. -3.... 1.... A200485
.. -3.... 2.... A200486
.. -3.... 3.... A200487
.. -3.... 4.... A200488
.. -4.... 1.... A200489
.. -4.... 2.... A200490
.. -4.... 3.... A200491
.. -4.... 4.... A200492
.. -1.... 1.... A200493
.. -1.... 2.... A200494
.. -1.... 3.... A200495
.. -1.... 4.... A200496
.. -2.... 1.... A200497
.. -2.... 3.... A200498
.. -3.... 1.... A200499
.. -3.... 2.... A200500
.. -3.... 3.... A200501
.. -3.... 4.... A200502
.. -4.... 1.... A200584
.. -4.... 3.... A200585
.. -1.... 2.... A200586
.. -1.... 3.... A200587
.. -1.... 4.... A200588
.. -2.... 1.... A200589
.. -2.... 2.... A200590
.. -2.... 3.... A200591
.. -2.... 4.... A200592
.. -3.... 1.... A200593
.. -3.... 2.... A200594
.. -3.... 4.... A200595
.. -4.... 1.... A200596
.. -4.... 2.... A200597
.. -4.... 3.... A200598
.. -4.... 4.... A200599
.. -1.... 1.... A200600
.. -1.... 2.... A200601
.. -1.... 3.... A200602
.. -1.... 4.... A200603
.. -2.... 1.... A200604
.. -2.... 3.... A200605
.. -3.... 1.... A200606
.. -3.... 2.... A200607
.. -3.... 3.... A200608
.. -3.... 4.... A200609
.. -4.... 1.... A200610
.. -4.... 3.... A200611
Suppose that f(x,u,v) is a function of three real variables and that g(u,v) is a function defined implicitly by f(g(u,v),u,v)=0.  We call the graph of z=g(u,v) an implicit surface of f.
For an example related to A200338, take f(x,u,v) = x^2 + u*x + v - tan(x) and g(u,v) = a nonzero solution x of f(x,u,v)=0. If there is more than one nonzero solution, care must be taken to ensure that the resulting function g(u,v) is single-valued and continuous.  A portion of an implicit surface is plotted by Program 2 in the Mathematica section.

			x=1.17209361728566903968781879581089880...

Index entries for transcendental numbers.

Cf. A197737, A198414, A198755, A198866, A199170, A199370, A199429, A199597, A199949.

(* Program 1:  A200338 *)
a = 1; b = 0; c = 1;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r]  (* A200338 *)
(* Program 2: implicit surface of x^2+u*x+v=tan(x) *)
f[{x_, u_, v_}] := x^2 + u*x + v - Tan[x];
t = Table[{u, v, x /. FindRoot[f[{x, u, v}] == 0, {x, 0, 1.57}]}, {u, 0, 5, .1}, {v, 0, 5, .1}];
ListPlot3D[Flatten[t, 1]]  (* for A200388 *)

solve(x=1,1.2,x^2+1-tan(x)) \\ Charles R Greathouse IV, Mar 23 2022

A199597 Decimal expansion of x > 0 satisfying x^2 + x*cos(x) = sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 08 2011

For many choices of a,b,c, there is exactly one x>0 satisfying a*x^2+b*x*cos(x)=c*sin(x).
Guide to related sequences, with graphs included in Mathematica programs:
a.... b.... c.... x
... 1.... 2.... A199597
... 1.... 3.... A199598
... 1.... 4.... A199599
... 2.... 1.... A199600
... 2.... 3.... A199601
... 2.... 4.... A199602
... 3.... 0.... A199603, A199604
... 3.... 1.... A199605, A199606
... 3.... 2.... A199607, A199608
... 3.... 3.... A199609, A199610
... 4.... 0.... A199611, A199612
... 4.... 1.... A199613, A199614
... 4.... 2.... A199615, A199616
... 4.... 3.... A199617, A199618
... 4.... 4.... A199619, A199620
... 1.... 0.... A199621
... 1.... 2.... A199622
... 1.... 3.... A199623
... 1.... 4.... A199624
... 2.... 1.... A199625
... 2.... 3.... A199661
... 1.... 0.... A199662
... 1.... 2.... A199663
... 1.... 3.... A199664
... 1.... 4.... A199665
... 2.... 0.... A199666
... 2.... 1.... A199667
... 2.... 3.... A199668
... 2.... 4.... A199669
.. -1.... 0.... A003957
.. -1.... 1.... A199722
.. -1.... 2.... A199721
.. -1.... 3.... A199720
.. -1.... 4.... A199719
.. -2.... 1.... A199726
.. -2.... 2.... A199725
.. -2.... 3.... A199724
.. -2.... 4.... A199723
.. -3.... 1.... A199730
.. -3.... 2.... A199729
.. -3.... 3.... A199728
.. -3.... 4.... A199727
.. -4.... 1.... A199737. A199738
.. -4.... 2.... A199735, A199736
.. -4.... 3.... A199733, A199734
.. -4.... 4.... A199731. A199732
.. -1.... 1.... A199742
.. -1.... 2.... A199741
.. -1.... 3.... A199740
.. -1.... 4.... A199739
.. -2.... 1.... A199776
.. -2.... 3.... A199775
.. -3.... 1.... A199780
.. -3.... 2.... A199779
.. -3.... 3.... A199778
.. -3.... 4.... A199777
.. -4.... 1.... A199782
.. -4.... 3.... A199781
.. -4.... 1.... A199786
.. -4.... 2.... A199785
.. -4.... 3.... A199784
.. -4.... 4.... A199783
.. -3.... 1.... A199789
.. -3.... 2.... A199788
.. -3.... 4.... A199787
.. -2.... 1.... A199793
.. -2.... 2.... A199792
.. -2.... 3.... A199791
.. -2.... 4.... A199790
.. -1.... 1.... A199797
.. -1.... 2.... A199796
.. -1.... 3.... A199795
.. -1.... 4.... A199794
.. -4.... 1.... A199873
.. -4.... 3.... A199872
.. -3.... 1.... A199871
.. -3.... 2.... A199870
.. -3.... 3.... A199869
.. -3.... 4.... A199868
.. -2.... 1.... A199867
.. -2.... 3.... A199866
.. -1.... 1.... A199865
.. -1.... 2.... A199864
.. -1.... 3.... A199863
.. -1.... 4.... A199862
Suppose that f(x,u,v) is a function of three real variables and that g(u,v) is a function defined implicitly by f(g(u,v),u,v)=0.  We call the graph of z=g(u,v) an implicit surface of f.
For an example related to A199597, take f(x,u,v)=x^2+u*x*cos(x)-v*sin(x) and g(u,v) = a nonzero solution x of f(x,u,v)=0.  If there is more than one nonzero solution, care must be taken to ensure that the resulting function g(u,v) is single-valued and continuous.  A portion of an implicit surface is plotted by Program 2 in the Mathematica section.

			1.1881851344514388032178109729076525973...

Index entries for transcendental numbers.

Cf. A199370, A199170, A198866, A198755, A198414, A197737, A199429.

(* Program 1:  A199597 *)
a = 1; b = 1; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.18, 1.19}, WorkingPrecision -> 110]
RealDigits[r]  (* A199597 *)
(* Program 2: impl. surf. x^2+u*x*cos(x)=v*sin(x) *)
f[{x_, u_, v_}] := x^2 + u*x*Cos[x] - v*Sin[x];
t = Table[{u, v, x /. FindRoot[f[{x, u, v}] == 0, {x, .5, 3}]}, {u, 0, 2}, {v, u, 20}];
ListPlot3D[Flatten[t, 1]]  (* for A199597 *)

Edited by Georg Fischer, Aug 03 2021

A199429 Decimal expansion of x>0 satisfying x^2+x*sin(x)=cos(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 06 2011

For many choices of a,b,c, there is exactly one x>0 satisfying a*x^2+b*x*sin(x)=c*cos(x).
Guide to related sequences, with graphs included in Mathematica programs:
a.... b.... c.... x
... 1.... 1.... A199429
... 1.... 2.... A199430
... 1.... 3.... A199431
... 2.... 1.... A199432
... 2.... 2.... A199433
... 2.... 3.... A199434
... 3.... 1.... A199435
... 3.... 2.... A199436
... 3.... 3.... A199437
... 1.... 1.... A199438
... 1.... 2.... A199439
... 1.... 3.... A199440
... 2.... 1.... A199441
... 2.... 3.... A199442
... 3.... 1.... A199443
... 3.... 2.... A199444
... 3.... 3.... A199445
... 1.... 1.... A199446
... 1.... 2.... A199447
... 1.... 3.... A199448
... 2.... 1.... A199449
... 2.... 2.... A199450
... 2.... 3.... A199451
... 3.... 1.... A199452
... 3.... 2.... A199453
.. -1.... 1.... A199454
.. -1.... 2.... A199455
.. -1.... 3.... A199456
.. -2... -3.... A199457
.. -2... -2.... A199458
.. -2... -1.... A199459
.. -2...  0.... A199460
.. -2...  1.... A199461
.. -2...  2.... A199462
.. -2...  3.... A199463
.. -3... -3.... A199464
.. -3... -2.... A199465
.. -3... -1.... A199466
.. -3...  0.... A199467
.. -3...  1.... A199468
.. -3...  2.... A199469
.. -3...  3.... A199470
.. -1...  1.... A199471
.. -1...  2.... A199472
.. -1...  3.... A199473
.. -2...  1.... A199503
.. -2...  3.... A199504
.. -1...  1.... A199505
.. -1...  2.... A199506
.. -1...  3.... A199507
.. -2...  1.... A199508
.. -2...  2.... A199509
.. -2...  3.... A199510
.. -3...  1.... A199511
.. -3...  2.... A199513
Suppose that f(x,u,v) is a function of three real variables and that g(u,v) is a function defined implicitly by f(g(u,v),u,v)=0.  We call the graph of z=g(u,v) an implicit surface of f.
For an example related to A199429, take f(x,u,v)=x^2+u*x*sin(x)-v*cos(x) and g(u,v) = a nonzero solution x of f(x,u,v)=0.  If there is more than one nonzero solution, care must be taken to ensure that the resulting function g(u,v) is single-valued and continuous.  A portion of an implicit surface is plotted by Program 2 in the Mathematica section.

			0.6434363641380261586420989143040131826874...

Index entries for transcendental numbers.

Cf. A199370, A199170, A198866, A198755, A198414, A197737.

(* Program 1:  A199429 *)
a = 1; b = 1; c = 1;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .64, .65}, WorkingPrecision -> 110]
RealDigits[r]  (* A199429 *)
(* Program 2: implicit surface: x^2+u*x*sin(x)=v*cos(x) *)
f[{x_, u_, v_}] := x^2 + u*x*Sin[x] - v*Cos[x];
t = Table[{u, v, x /. FindRoot[f[{x, u, v}] == 0, {x, 0, 1}]}, {u, 0, 10}, {v, u, 100}];
ListPlot3D[Flatten[t, 1]]  (* for A199429 *)

g(a,b,c)=solve(x=0,abs(a)+abs(b)+abs(c), my(S=sin(x),C=sqrt(1-s^2)); a*x^2+b*x*S-c*C)
g(1,1,1) \\ Charles R Greathouse IV, Feb 07 2025

A199370 Decimal expansion of x>0 satisfying x^2+x*sin(x)=1.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 05 2011

For many choices of a,b,c, there is exactly one x>0 satisfying a*x^2+b*x*sin(x)=c.
Guide to related sequences, with graphs included in Mathematica programs:
a.... b.... c.... x
... 1.... 1.... A199370
... 1.... 2.... A199371
... 1.... 3.... A199372
... 2.... 1.... A199373
... 2.... 2.... A199374
... 2.... 3.... A199375
... 3.... 1.... A199376
... 3.... 2.... A199377
... 3.... 3.... A199378
... 1.... 1.... A199379
... 1.... 2.... A199180
... 1.... 3.... A199181
... 2.... 1.... A199182
... 2.... 3.... A199183
... 3.... 1.... A199184
... 3.... 2.... A199185
... 3.... 3.... A199186
... 1.... 1.... A199187
... 1.... 2.... A199188
... 1.... 3.... A199189
... 2.... 1....
... 2.... 2....
... 2.... 3....
... 3.... 1....
... 3.... 2....
Suppose that f(x,u,v) is a function of three real variables and that g(u,v) is a function defined implicitly by f(g(u,v),u,v)=0.  We call the graph of z=g(u,v) an implicit surface of f.
For an example related to A199370, take f(x,u,v)=x^2+u*x*sin(x)-v and g(u,v) = a nonzero solution x of f(x,u,v)=0.  If there is more than one nonzero solution, care must be taken to ensure that the resulting function g(u,v) is single-valued and continuous.  A portion of an implicit surface is plotted by Program 2 in the Mathematica section.

			0.722587549922524768355932872877196755159...

Index entries for transcendental numbers.

Cf. A199371, A199170, A198866, A198755, A198414, A197737.

(* Program 1: A199370 *)
a = 1; b = 1; c = 1;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -1, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .72, .73}, WorkingPrecision -> 110]
RealDigits[r]  (* A199370 *)
(* Program 2: implicit surface of x^2+u*x*sin(x)=v *)
f[{x_, u_, v_}] := x^2 + u*x*Sin[x] - v;
t = Table[{u, v, x /. FindRoot[f[{x, u, v}] == 0, {x, 0, 1}]}, {u, 0, 2.9}, {v, u, 600}];
ListPlot3D[Flatten[t, 1]]  (* for A199370 *)

A199180 Decimal expansion of x<0 satisfying x^2+2xcos(x)=3.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 04 2011

See A199170 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -1.6524280450417421424058918662580123...
positive:  2.980645279438536834594908905579032175...

Index entries for transcendental numbers.

Cf. A199170.

a = 1; b = 2; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199180 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.98, 2.99}, WorkingPrecision -> 110]
RealDigits[r]  (* A199181 *)

A199181 Decimal expansion of x>0 satisfying x^2+2xcos(x)=3.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 04 2011

See A199170 for a guide to related sequences. The Mathematica program includes a graph.

			negative: -1.6524280450417421424058918662580123...
positive:  2.980645279438536834594908905579032175...

Index entries for transcendental numbers.

Cf. A199170.

a = 1; b = 2; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199180 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.98, 2.99}, WorkingPrecision -> 110]
RealDigits[r]  (* A199181 *)

A199182 Decimal expansion of least x satisfying x^2+3xcos(x)=1.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 04 2011

See A199170 for a guide to related sequences. The Mathematica program includes a graph.

			least: -1.3606727725137972152286027487379925...
greatest: 3.27746466341373058734587727791083...

Index entries for transcendental numbers.

Cf. A199170.

a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]
RealDigits[r]   (* A199182  least of four roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.27, 3.28}, WorkingPrecision -> 110]
RealDigits[r]  (* A199183   greatest of four roots *)

A199183 Decimal expansion of greatest x satisfying x^2 + 3xcos(x) = 1.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 04 2011

See A199170 for a guide to related sequences. The Mathematica program includes a graph.

			least: -1.3606727725137972152286027487379925...
greatest: 3.27746466341373058734587727791083...

Index entries for transcendental numbers.

Cf. A199170, A199182.

a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]
RealDigits[r]   (* A199182  least of four roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.27, 3.28}, WorkingPrecision -> 110]
RealDigits[r]   (* A199183  greatest of four roots *)

a(92) onwards corrected by Georg Fischer, Aug 03 2021

A199184 Decimal expansion of least x satisfying x^2+3xcos(x)=2.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 04 2011

See A199170 for a guide to related sequences. The Mathematica program includes a graph.

			least: -1.5093390624666881234512526417921902931351...
greatest: 3.44428460990495541079195552785381251956...

Index entries for transcendental numbers.

Cf. A199170.

a = 1; b = 3; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.6, -1.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199184 least of four roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.44, 3.45}, WorkingPrecision -> 110]
RealDigits[r]  (* A199185 greatest of four roots *)

A199185 Decimal expansion of greatest x satisfying x^2+3xcos(x)=2.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 04 2011

See A199170 for a guide to related sequences. The Mathematica program includes a graph.

			least: -1.5093390624666881234512526417921902931351...
greatest: 3.44428460990495541079195552785381251956...

Index entries for transcendental numbers.

Cf. A199170.

a = 1; b = 3; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.6, -1.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199184  least of four roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.44, 3.45}, WorkingPrecision -> 110]
RealDigits[r]  (* A199185   greatest of four roots *)

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A199183 Decimal expansion of greatest x satisfying x^2 + 3*x*cos(x) = 1.

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A199181 Decimal expansion of x>0 satisfying x^2+2xcos(x)=3.

A199182 Decimal expansion of least x satisfying x^2+3xcos(x)=1.

A199183 Decimal expansion of greatest x satisfying x^2 + 3xcos(x) = 1.

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