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A354585
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Least prime p such that 2^x - 2 + p produces primes for x=1..n and a composite for x=n+1.
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1
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2, 3, 11, 5, 227, 17, 65837, 1607, 19427, 2397347207, 153535525937, 157542769194527, 29503289812427, 32467505340816977, 1109038455070356527, 143924005810811657, 305948728878647722727
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OFFSET
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1,1
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COMMENTS
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This sequence is a variation of A164926.
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LINKS
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EXAMPLE
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For n=5, 227 is the smallest prime such that 2^x - 2 + p produces primes for x=1..n and a composite for x=n+1. The following are the 5 primes that are produced: 227, 229, 233, 241, 257; note that the consecutive differences are 2, 4, 8, and 16.
For n=6, 17 is the smallest prime such that 2^x - 2 + p produces primes for x=1..n and a composite for x=n+1. The following are the 6 primes that are produced: 17, 19, 23, 31, 47, 79; note that the consecutive differences are 2, 4, 8, 16, and 32.
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PROG
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(Python)
import sympy
def get_longest_run_of_primes(p):
run = [p]
x = 2
while True:
next_prime = 2**x - 2 + p
if sympy.isprime(next_prime):
run.append(next_prime)
x = x + 1
else:
break
return run
n_to_longest_run_map = {}
max_prime_index = 100000
for prime_index in range(1, max_prime_index+1):
p = sympy.prime(prime_index)
longest_run_for_p = get_longest_run_of_primes(p)
length_of_longest_run_for_p = len(longest_run_for_p)
if length_of_longest_run_for_p not in n_to_longest_run_map:
n_to_longest_run_map[length_of_longest_run_for_p] = longest_run_for_p
n = 1
seq = []
while n in n_to_longest_run_map:
seq.append(n_to_longest_run_map[n][0])
n = n + 1
print(seq)
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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