A385636 Numbers k where sin(sqrt(k)) reaches successive record high values.

0, 1, 2, 60, 61, 62, 200, 417, 2687, 1536009, 57157270, 81436635, 143005063, 706132910, 2016118929

Offset: 1

Author

Artur Jasinski, Jul 05 2025

Keywords

• nonn
• more

Comments

Each record value is ever closer to 1, but never reaches 1 since Pi is not algebraic.

Examples

			         n sin(sqrt(n))
         0 0.00000000000000000000000000000000000000
         1 0.84147098480789650665250232163029899962
         2 0.98776594599273552706913407207894265590
        60 0.99417205583623141588832072787265937649
        61 0.99904391031188045397420593007730566087
        62 0.99979948155661636906716009313812999866
       200 0.99998765612212040379361805662023274661
       417 0.99999997455044116794629686048124083679
      2687 0.99999999999810547903298251324014875470
   1536009 0.99999999999999044600166587966774547198
  57157270 0.99999999999999422252795052032516595669
  81436635 0.99999999999999964054666338696864815400
 143005063 0.99999999999999999572901646060974247156
 706132910 0.99999999999999999879205185535546721950
2016118929 0.99999999999999999996673765988843841836
		

Crossrefs

Cf. A046959, A046964, A046965.

Programs

Mathematica

max = -2; aa = {}; Do[kk = N[Sin[Sqrt[n]], 50]; If[kk > max, max = kk; Print[{n, kk}]; AppendTo[aa, n]], {n, 0, 150000000}]; aa

Extensions

a(14)-a(15) from David Consiglio, Jr., Jul 14 2025