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
Keywords
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
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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