%I
%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[n1][[1]]+1; steps=0; While[!PrimeQ[k]  k <= f[n1][[2]], k=2k+1; steps++]; {start, k, steps}); A051918 = Table[Print[f[n] // Last]; f[n], {n, 0, 13}][[All, 3]] (* _JeanFrançois 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
