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

0,1

Links

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

Example

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

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:

Prog

(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

Crossrefs

Cf. A230225.

Sequence in context: A298039 A376828 A135659 * A255414 A031388 A163354

Adjacent sequences: A337751 A337752 A337753 * A337755 A337756 A337757

Keyword

nonn

Author

Michel Lagneau, Sep 21 2020

Status

approved