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A124013
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Lesser of pair of most widely separated primes whose sum is 10^n.
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3
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3, 3, 3, 59, 11, 17, 29, 11, 71, 71, 23, 11, 29, 29, 11, 83, 3, 11, 281, 11, 101, 71, 23, 257, 401, 293, 107, 293, 53, 11, 113, 251, 47, 587, 23, 179, 389, 59, 173, 17, 1427, 83, 431, 53, 563, 593, 41, 47, 239, 383, 431, 1181, 701, 971, 149, 593, 569, 149, 191, 1973
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OFFSET
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1,1
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COMMENTS
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For any n>=1 the sequence gives the minimum prime p such that 10^n-p is also a prime. - Paolo P. Lava and Giorgio Balzarotti, Feb 25 2008
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LINKS
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Table of n, a(n) for n=1..60.
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FORMULA
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10^n - a(n) is prime and 10^n - k is composite for 0 <= k < a(n). - corrected by David A. Corneth, Aug 18 2016
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EXAMPLE
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10^1 = 3 + 7, 10^2 = 3 + 97, 10^3 = 3 + 997, 10^4 = 59 + 9941, 10^5 = 11 + 99989, 10^6 = 17 + 999983, 10^7 = 29 + 9999971, 10^8 = 11 + 99999989, 10^9 = 71 + 999999929, 10^10 = 71 + 9999999929, etc.
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MAPLE
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P:=proc(n) local a, i, k; for i from 0 by 1 to n do k:=1; while ithprime(k)<10^i do a:=10^i-ithprime(k); if isprime(a) then print(ithprime(k)); break; fi; k:=k+1; od; od; end: P(1000); # Paolo P. Lava and Giorgio Balzarotti, Feb 25 2008
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MATHEMATICA
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Table[DeleteCases[Map[{#, 10^n - #} &, Prime@ Range@ PrimePi@ Floor[10^n/2]] /. {_, k_} /; ! PrimeQ@ k -> 0, 0][[1, 1]], {n, 8}] (* or *)
Table[First@ SelectFirst[Map[{#, 10^n - #} &, Prime@ Range@ PrimePi@ Floor[10^n/2]], PrimeQ@ Last@ # &], {n, 9}] (* Version 10, Michael De Vlieger, Aug 01 2016 *)
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CROSSREFS
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Cf. A065577 (Number of Goldbach partitions of 10^n), A124450 (Lesser of pair of closest primes summed to 10^n).
Sequence in context: A122092 A230495 A025549 * A135584 A174538 A340821
Adjacent sequences: A124010 A124011 A124012 * A124014 A124015 A124016
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov, Nov 02 2006
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EXTENSIONS
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a(1) corrected and a(2) inserted by Gionata Neri, Aug 01 2016
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STATUS
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approved
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