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A051918 Start with n, apply k->2k+1 until reach new record prime; sequence gives number of steps needed. 2
2, 2, 2, 3, 4, 5, 5, 10, 13, 13, 26, 32, 287, 18380, 21727, 23205, 24828, 35646, 48819, 51476 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..19.

EXAMPLE

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.

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-Fran├žois Alcover, Dec 10 2014 *)

CROSSREFS

Cf. A051919, A052333.

Sequence in context: A029074 A258741 A036016 * A174740 A163801 A323735

Adjacent sequences:  A051915 A051916 A051917 * A051919 A051920 A051921

KEYWORD

nice,nonn,hard

AUTHOR

N. J. A. Sloane, Dec 18 1999

EXTENSIONS

More terms from Naohiro Nomoto, May 21 2001

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

STATUS

approved

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Last modified October 21 13:24 EDT 2019. Contains 328299 sequences. (Running on oeis4.)