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

Author

N. J. A. Sloane, Aug 05 2024

Keywords

• nonn

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) 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

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..2000
• N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]

Crossrefs

Cf. A374965, A076336, A101036.

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

Programs

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 *)

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