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A331861
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Numbers n for which R(n) + 10^floor(n/2) is prime, where R(n) = (10^n-1)/9.
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4
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OFFSET
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1,2
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COMMENTS
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The primes corresponding to the terms of the sequence are a subset of the near-repunit primes A105992.
In base 10, R(n) + 10^floor(n/2) has ceiling(n/2)-1 digits 1, one digit 2, and again floor(n/2) digits 1. For odd n, this is a palindrome, for even n the digit 2 is just left to the middle of the number.
There cannot be an odd term > 1 since the corresponding palindrome factors as R((n+1)/2)*(10^((n-1)/2) + 1).
No term can be congruent to 2 mod 3. - Chai Wah Wu, Feb 07 2020
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LINKS
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EXAMPLE
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For n = 1, R(n) + 10^floor(n/2) = 2 is prime.
For n = 6, R(n) + 10^floor(n/2) = 112111 is prime.
For n = 10, R(n) + 10^floor(n/2) = 1111211111 is prime.
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PROG
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(PARI) for(n=0, 9999, isprime(p=10^n\9+10^(n\2))&&print1(n", "))
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CROSSREFS
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Cf. A331860 (variant with floor(n/2-1) instead of floor(n/2)), A331862 (variant with - (digit 0) instead of + (digit 2)).
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KEYWORD
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nonn,more,hard,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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