

A124013


Lesser of pair of most widely separated primes whose sum is 10^n.


3



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

1,1


COMMENTS

For any n>=1 the sequence gives the minimum prime p such that 10^np is also a prime.  Paolo P. Lava and Giorgio Balzarotti, Feb 25 2008


LINKS

Table of n, a(n) for n=1..60.


FORMULA

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


EXAMPLE

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.


MAPLE

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^iithprime(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


MATHEMATICA

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 *)


CROSSREFS

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


KEYWORD

nonn


AUTHOR

Zak Seidov, Nov 02 2006


EXTENSIONS

a(1) corrected and a(2) inserted by Gionata Neri, Aug 01 2016


STATUS

approved



