A051918 Start with n, apply k->2k+1 until reach new record prime; sequence gives number of steps needed.

2, 2, 2, 3, 4, 5, 5, 10, 13, 13, 26, 32, 287, 18380, 21727, 23205, 24828, 35646, 48819, 51476

Offset: 0

Author

N. J. A. Sloane, Dec 18 1999

Keywords

• nice
• nonn
• hard

Comments

a(20) > 60000. [From Donovan Johnson, May 23 2010]

Examples

			0->1->3, new record prime 3 in 2 steps; 1->3->7, new record prime 7 in 2 steps; 2->5->11, new record prime 11 in 2 steps; 3->7->15->31, new record prime 31 in 3 steps.
For the next few terms we have: 4->9->19->39->79; 5->11->23->47->95->191; 6->13->27->55->111->223; 7->15->31->63->127->255->511->1023->2047->4095->8191; etc.
		

Crossrefs

Cf. A051919, A052333.

Programs

Mathematica

f[0] = {start=0, k=3, steps=2}; f[n_] := f[n] = (k=start=f[n-1][[1]]+1; steps=0; While[!PrimeQ[k] || k <= f[n-1][[2]], k=2k+1; steps++]; {start, k, steps}); A051918 = Table[Print[f[n] // Last]; f[n], {n, 0, 13}][[All, 3]] (* Jean-François Alcover, Dec 10 2014 *)

Extensions

More terms from Naohiro Nomoto, May 21 2001

a(13)-a(19) from Donovan Johnson, May 23 2010