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A331866
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Numbers k for which R(k) + 3*10^floor(k/2) is prime, where R(k) = (10^k-1)/9 (repunit: A002275).
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3
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0, 2, 5, 7, 8, 10, 65, 91, 208, 376, 586, 2744, 3089, 19378
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OFFSET
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1,2
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COMMENTS
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The corresponding primes are a subset of the near-repunit primes A105992 (at least when they have k > 2 digits).
In base 10, R(k) + 3*10^floor(k/2) has k digits all of which are 1 except for one digit 4 (for k > 0) located in the center (for odd k) or just to the left of it (for even k): i.e., there are ceiling(k/2)-1 digits 1 to the left and floor(k/2) digits 1 to the right of the digit 4. For odd k, this is a palindrome a.k.a. wing prime, cf. A077780, the subsequence of odd terms.
a(14) = 19378 was found by Amiram Eldar, verified to be the 14th term in collaboration with the author of the sequence and factordb.com. The term a(13) = 3089 corresponds to a certified prime (Ivan Panchenko, 2011, cf. factordb.com); a(12) and a(14) are only PRP as far as we know.
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LINKS
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EXAMPLE
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For n = 0, R(0) + 3*10^floor(0/2) = 3 is prime.
For n = 2, R(2) + 3*10^floor(2/2) = 41 is prime.
For n = 5, R(5) + 3*10^floor(5/2) = 11411 is prime.
For n = 7, R(7) + 3*10^floor(7/2) = 1114111 is prime.
For n = 8, R(8) + 3*10^floor(8/2) = 11141111 is prime.
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MATHEMATICA
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Select[Range[0, 2500], PrimeQ[(10^# - 1)/9 + 3*10^Floor[#/2]] &]
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PROG
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(PARI) for(n=0, 9999, ispseudoprime(p=10^n\9+3*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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STATUS
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approved
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