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A331869
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Numbers n for which R(n) + 4*10^floor(n/2) is prime, where R(n) = (10^n-1)/9 (repunit: A002275).
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3
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1, 3, 4, 15, 76, 91, 231, 1363, 1714, 1942, 2497, 4963, 5379, 12397, 23224, 26395
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OFFSET
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1,2
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COMMENTS
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For n > 1, the corresponding primes are a subset of A105992: near-repunit primes.
In base 10, R(n) + 4*10^floor(n/2) has ceiling(n/2)-1 digits 1, one digit 5, and again floor(n/2) digits 1, except for n = 0. For odd n, this is a palindrome (a.k.a. wing prime, cf. A077783: subsequence of odd terms), for even n the digit 5 is just left to the middle of the number.
See also the variant A331868 where the digit 5 is just to the right of the middle.
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LINKS
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EXAMPLE
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For n = 1, R(1) + 4*10^floor(1/2) = 5 is prime.
For n = 3, R(3) + 4*10^floor(3/2) = 151 is prime.
For n = 4, R(4) + 4*10^floor(4/2) = 1511 is prime.
For n = 15, R(15) + 4*10^floor(15/2) = 111111151111111 is prime.
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MATHEMATICA
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Select[Range[0, 2500], PrimeQ[(10^# - 1)/9 + 4*10^Floor[#/2]] &]
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PROG
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(PARI) for(n=0, 9999, ispseudoprime(p=10^n\9+4*10^(n\2))&&print1(n", "))
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CROSSREFS
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KEYWORD
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nonn,base,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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