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A337754
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Least prime p such that 2p+1, 2p+3,..., 2p+2n+1 are not prime.
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1
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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
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OFFSET
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0,1
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LINKS
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EXAMPLE
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a(1) = 31 because 2*31+1=63 and 2*31+3=65 are not prime.
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MAPLE
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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:
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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