A373801 - OEIS

%I #41 Aug 09 2024 23:12:42

%S 2,4,7,8,15,29,18,35,69,137,32,63,125,249,497,993,1985,3969,7937,72,

%T 143,285,569,90,179,102,203,405,809,114,227,132,263,140,279,557,158,

%U 315,629,1257,2513,5025,10049,20097,40193,200,399,797,228,455,909,1817,3633,7265,14529,29057,58113,116225

%N a(1) = 2; thereafter, if a(n-1) is prime then a(n) = prime(n) + 1; otherwise a(n) = 2*a(n-1) - 1.

%C Inspired by A374965. Just as the Riesel numbers (A101036 etc.) underlie A374965, so the Sierpinski numbers (A076336 etc.) underlie the present sequence. This means that for both A374965 and the present sequence, it is possible that there are only finitely many prime terms.

%C What is the next prime after a(1336) = 1486047139543908353?

%C The next prime in the sequence after a(1336) is the 328-digit prime a(2412) = 11027*2^1075 + 1 =

%C 44637792944394283771459323765390022896709223538983902782431025499369487088325693\

%C 80355294302151494343616855815219642969893790841894306289338825113522293047097809\

%C 14527499539453353195318334412379318970183638103791974206651303944817277532365140\

%C 54865648555402249863235603037071611259242935028448372668756790221309881865220759\

%C 33966337. - _Alois P. Heinz_, Aug 05 2024

%C For a(1) any prime, the trajectory converges to this sequence. Just as in A374965, the trajectories appear to converge to a few attractors. In fact it appears that for most values of a(1), the trajectory converges to the present sequence. However, for a(1) = 384 and 767 the trajectories are different. - _Chai Wah Wu_, Aug 07 2024

%H N. J. A. Sloane, <a href="/A373801/b373801.txt">Table of n, a(n) for n = 1..2000</a>

%p A:=Array(1..1200,0);

%p t:=2;

%p A[1]:= t;

%p for n from 2 to 100 do

%p if isprime(t) then t:=ithprime(n)+1; else t:=2*t-1; fi;

%p A[n]:=t;

%p od:

%p [seq(A[n],n=1..100)];

%t Module[{n = 1}, NestList[If[n++; PrimeQ[#], Prime[n] + 1, 2*# - 1] &, 2, 100]] (* _Paolo Xausa_, Aug 07 2024 *)

%o (Python)

%o from sympy import isprime, nextprime

%o def A373801_gen(): # generator of terms

%o     a, p = 2, 3

%o     while True:

%o         yield a

%o         a, p = p+1 if isprime(a) else (a<<1)-1, nextprime(p)

%o A373801_list = list(islice(A373801_gen(),20)) # _Chai Wah Wu_, Aug 05 2024

%Y Cf. A374965, A076336, A101036.

%Y For the primes in this sequence, see A373802 and A373803.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Aug 05 2024