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%I #10 Dec 10 2014 09:16:44
%S 2,2,2,3,4,5,5,10,13,13,26,32,287,18380,21727,23205,24828,35646,48819,
%T 51476
%N Start with n, apply k->2k+1 until reach new record prime; sequence gives number of steps needed.
%C a(20) > 60000. [From _Donovan Johnson_, May 23 2010]
%e 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.
%e 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.
%t 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 *)
%Y Cf. A051919, A052333.
%K nice,nonn,hard
%O 0,1
%A _N. J. A. Sloane_, Dec 18 1999
%E More terms from _Naohiro Nomoto_, May 21 2001
%E a(13)-a(19) from _Donovan Johnson_, May 23 2010
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