A364091 - OEIS

A364091

a(n) is the first prime p such that the longest sequence of primes p = p_1, p_2, ... with |p_{k+1} - 2*p_k| = 1 has length n.

13, 7, 11, 5, 3, 2, 16651, 15514861, 85864769, 26089808579, 665043081119, 554688278429, 758083947856951, 95405042230542329, 69257563144280941

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) = A000040(k) where A263879(k) = n is the first appearance of n in A263879.

LINKS

Table of n, a(n) for n=1..15.

FORMULA

a(n) = min(A005602(n), A005603(n)) for n >= 7.

EXAMPLE

a(4) = 5 because 5, 2*5 + 1 = 11, 2*11 + 1 = 23, 2*23 + 1 = 47 is a sequence of primes of length 4 while 2*47 - 1 = 93 and 2*47 + 1 = 95 are not primes, and 5 is the smallest prime that works.

MAPLE

M:= 10: # for a(1) .. a(N)

f:= proc(n) option remember; local x;

if n mod 3 = 1 then x:= 2*n-1 else x:= 2*n+1 fi;

if isprime(x) then 1 + procname(x) else 1 fi;

end proc:

f(2):= 6: f(3):= 5:

V:= Vector(M):

p:= 1: count:= 0:

for k from 1 while count < M do

p:= nextprime(p);

v:= f(p);

if v <= M and V[v] = 0 then V[v]:= p; count:= count+1; fi

od:

convert(V, list);

PROG

(Python)

from sympy import isprime, nextprime

def A364091(n):

if 5 <= n <= 6: return 8-n

q = 5

while True:

p, c = q, 1

while isprime(p:=(p<<1)+(-1 if p%3==1 else 1)):

c += 1

if c > n:

break

if c == n:

return q

q = nextprime(q) # Chai Wah Wu, Jul 07 2023

CROSSREFS

Cf. A000040, A263879.

Sequence in context: A222464 A095389 A217518 * A257928 A206611 A345399

Adjacent sequences: A364088 A364089 A364090 * A364092 A364093 A364094

KEYWORD

nonn,more

AUTHOR

Robert Israel, Jul 04 2023

STATUS

approved