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A359952
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Wieferich sequence where a(1) = 2.
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0
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2, 1093, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043, 5, 20771, 18043
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OFFSET
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1,1
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COMMENTS
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Starting with a(3), the sequence is periodic with the following cycle, which is a Wieferich triplet: 5, 20771, 18043.
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LINKS
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PROG
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(Python)
from sympy import nextprime
from gmpy2 import powmod
max_n = 45
a = 2
seq = [a]
for i in range(2, max_n+1):
p = 2
while True:
p_squared = p*p
if powmod(a, p-1, p_squared) == 1 and (a-1) % p_squared != 0 and (a+1) % p_squared != 0:
seq.append(p)
a = p
break
else:
p = nextprime(p)
print(seq)
(PARI) i=0; a=2; print1(a, ", "); while(i<100, forprime(p=2, 10^6, if(Mod(a, p^2)^(p-1)==1 && p%2!=0 && ((a-1) % p^2) && ((a+1) % p^2), print1(p, ", "); i++; a=p; break({n=1})))) \\ Michel Marcus, Jan 21 2023
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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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