%I
%S 3,7,11,31,79,191,223,8191,73727,81919,738197503,51539607551,
%T 3232601036663613174009984612954335460652964980182760163363015849805536730581466940964863
%N Start with n, apply k>2k+1 until reach new record prime; sequence gives record primes.
%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; ...
%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}); A051919 = Table[Print[f[n] // Last]; f[n], {n, 0, 12}][[All, 2]] (* _JeanFrançois Alcover_, Dec 10 2014 *)
%Y Cf. A051918, A052333.
%K nice,nonn
%O 0,1
%A _N. J. A. Sloane_, Dec 18 1999
%E More terms from _Naohiro Nomoto_, May 21 2001, who reports that the next term is > 10^130.
