A337754 Least prime p such that 2p+1, 2p+3,..., 2p+2n+1 are not prime.

7, 31, 59, 59, 263, 263, 263, 691, 977, 1091, 1487, 1487, 2417, 2797, 4987, 4987, 6427, 9811, 9811, 12739, 12739, 12739, 17033, 17033, 17033, 17033, 17033, 17033, 67261, 77969, 77969, 77969, 77969, 77969, 140717, 140717, 140717, 169019, 169019, 169019, 180331

Offset: 0

Author

Michel Lagneau, Sep 21 2020

Keywords

• nonn

Examples

			a(1) = 31 because 2*31+1=63 and 2*31+3=65 are not prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..207

Crossrefs

Cf. A230225.

Programs

Maple

nn:=10^8:
for n from 1 to 50 do:
ii:=0:
  for k from 2 to nn while(ii=0)do:
    p:=ithprime(k):jj:=0:
     for i from 1 by 2 to 2*n-1 do:
      if isprime(2*p+i)
       then
       jj:=1:
       else
      fi:
     od:
       if jj=0
        then
        ii:=1: printf(`%d, `,p):
        else
       fi:
     od:
   od:

PARI

isok(p, n) = {forstep(k=1, 2*n+1, 2, if (isprime(2*p+k), return (0));); return(1);}
a(n) = {my(p=2); while(!isok(p, n), p = nextprime(p+1)); p;} \\ Michel Marcus, Sep 21 2020

Python

from sympy import isprime, nextprime
def a(n, startp=2):
    p = startp
    while any(isprime(2*p+i) for i in range(1, 2*n+2, 2)): p = nextprime(p)
    return p
print([a(n) for n in range(41)]) # Michael S. Branicky, Jul 31 2021

Python

# uses above to produce initial segment faster
def aupton(nn):
    an, alst = 2, []
    for n in range(nn+1): an = a(n, startp=an); alst.append(an)
    return alst
print(aupton(40)) # Michael S. Branicky, Jul 31 2021