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A105120 a(1) = 2; k(1) = 0; for n > 1: k(n) = smallest number j >= k(n-1) such that 2*a(n-1) + j is prime; a(n) = 2*a(n-1) + k(n).

%I A105120 #15 Feb 21 2022 23:48:33
%S A105120 2,5,11,23,47,97,197,397,797,1597,3203,6421,12889,25841,51749,103567,
%T A105120 207227,414553,829211,1658533,3317177,6634469,13269059,26538257,
%U A105120 53076679,106153547,212307299,424614829,849229907,1698460067,3396920419
%N A105120 a(1) = 2; k(1) = 0; for n > 1: k(n) = smallest number j >= k(n-1) such that 2*a(n-1) + j is prime; a(n) = 2*a(n-1) + k(n).
%C A105120 Numbers k(n) are given in A105121.
%C A105120 a(n) appears to tend toward C*A055496(n), C~ 0.992521946129820000. - _Bill McEachen_, Feb 21 2022
%H A105120 Robert G. Wilson v, <a href="/A105120/b105120.txt">Table of n, a(n) for n = 1..3000.</a>.
%e A105120 a(10) = 1597; k(10) = 3; 2*1597 + j is not prime for 3 <= j < 9, but 2*1597 + 9 = 3203 is prime. Hence k(11) = 9 and a(11) = 3203.
%t A105120 a[1] = {2, 0}; a[n_] := a[n] = Block[{m = 2a[n - 1][[1]], k = a[n - 1][[2]]}, While[ !PrimeQ[m + k], k++ ]; {m + k, k}]; Table[ a[n][[1]], {n, 30}] (* _Robert G. Wilson v_, Apr 08 2005 *)
%o A105120 (PARI) print1(a=2,","); k=0; for(n=2,31, j=k; while(!isprime(2*a+j),j++); k=j; print1(a=2*a+k,",")) \\ _Klaus Brockhaus_, Apr 08 2005
%Y A105120 k(n) is in A105121.
%K A105120 nonn
%O A105120 1,1
%A A105120 _Yasutoshi Kohmoto_, Apr 08 2005
%E A105120 Edited, corrected and extended by _Klaus Brockhaus_ and _Robert G. Wilson v_, Apr 08 2005