A373801 a(1) = 2; thereafter, if a(n-1) is prime then a(n) = prime(n) + 1; otherwise a(n) = 2*a(n-1) - 1.

2, 4, 7, 8, 15, 29, 18, 35, 69, 137, 32, 63, 125, 249, 497, 993, 1985, 3969, 7937, 72, 143, 285, 569, 90, 179, 102, 203, 405, 809, 114, 227, 132, 263, 140, 279, 557, 158, 315, 629, 1257, 2513, 5025, 10049, 20097, 40193, 200, 399, 797, 228, 455, 909, 1817, 3633, 7265, 14529, 29057, 58113, 116225

Offset

1,1

Comments

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.

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

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

44637792944394283771459323765390022896709223538983902782431025499369487088325693\

80355294302151494343616855815219642969893790841894306289338825113522293047097809\

14527499539453353195318334412379318970183638103791974206651303944817277532365140\

54865648555402249863235603037071611259242935028448372668756790221309881865220759\

33966337. - Alois P. Heinz, Aug 05 2024

For a(1) prime, the trajectory converges to this sequence. Similar to A374965, the trajectories appear to converge to a few attractors. It appears that for most values of a(1), the trajectory converges to this sequences. For a(1) = 384 and 767, the trajectories traversed are different. - Chai Wah Wu, Aug 07 2024

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..2000

Maple

A:=Array(1..1200, 0);
t:=2;
A[1]:= t;
for n from 2 to 100 do
if isprime(t) then t:=ithprime(n)+1; else t:=2*t-1; fi;
A[n]:=t;
od:
[seq(A[n], n=1..100)];

Mathematica

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

Prog

(Python)
from sympy import isprime, nextprime
def A373801_gen(): # generator of terms
    a, p = 2, 3
    while True:
        yield a
        a, p = p+1 if isprime(a) else (a<<1)-1, nextprime(p)
A373801_list = list(islice(A373801_gen(), 20)) # Chai Wah Wu, Aug 05 2024

Crossrefs

Cf. A374965, A076336, A101036.

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

Sequence in context: A056694 A090606 A241548 * A019539 A327099 A338888

Adjacent sequences: A373798 A373799 A373800 * A373802 A373803 A373804

Keyword

nonn,new

Author

N. J. A. Sloane, Aug 05 2024

Status

approved