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%I #20 May 16 2014 15:44:53
%S 2,11,113,1117,11113,111119,1111379,11111117,111111113,1111111973,
%T 11111111113,111111111379,1111111111717,11111111111719,
%U 111111111111713,1111111111111319,11111111111111119,111111111111111131
%N Least n-digit prime in which every two-digit string is also a prime, or 0 if no such number exists. (n-1 two-digit string primes occur.)
%C Conjecture: sequence is infinite. Notes: (1) If n==1 (mod 3) then in most cases a(n) is a permutation of (n-1), 1's and a 7, else a(n) is a digit permutation of (n-1) ones and a 3; (2) Obviously all the digits except the most significant one must be odd.
%C The least potential candidate, lpc(n), is of the form (10^n-1)/9. The following is a(n)-lpc(n): 1, 0, 2, 6, 2, 8, 268, 6, 2, 862, 2, 268, 606, 608, 602, 208, 8, 20, 0, 20, 68, 600, 0, 2, 606, .... - _Robert G. Wilson v_, May 12 2014
%H Robert G. Wilson v, <a href="/A090534/b090534.txt">Table of n, a(n) for n = 1..100</a>
%e a(5) = 11113 in which 11,11,11,13 are the two-digit string primes.
%t fQ[p_] := Block[{id = IntegerDigits@ p}, Union@ PrimeQ[ FromDigits@# & /@ Partition[id, 2, 1]] == {True}]; f[n_] := Block[{p = NextPrime[(10^n - 1)/9 - 1]}, While[! fQ@ p, p = NextPrime@ p]; p]; f[1] = 2; Array[ f, 19] (* _Robert G. Wilson v_, May 12 2014 *)
%Y Cf. A242377.
%K base,nonn
%O 1,1
%A _Amarnath Murthy_, Dec 08 2003
%E More terms from _David Wasserman_, Dec 21 2005
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