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%I #17 Sep 16 2018 02:11:22
%S 0,1,4,6,7,9,12,13,15,18,19,22,25,28,31,33,39,46,48,49,52,60,61,64,67,
%T 73,75,84,85,88,90,99,100,103,106,132,133,135,136,138,142,156,160,163,
%U 171,178,181,183,187,190,198,201,202,211,220,222,229,238,241,246,252
%N Numbers n such that (n+2)//n - (n+1) is prime, where // represents the concatenation of decimals.
%C If n is a k-digit number, then we demand that p = (n+2) * 10^k + n - (n+1) is a prime number, obviously of the form p = (n+2) * 10^k - 1, so the decimal representation of p is n+1 followed by k times the digit 9.
%C The sequence is infinite, proof with Dirichlet's prime number (in arithmetic progressions) theorem.
%C Note that numbers of the form (n+2)//n + (n+1) are multiples of 3 and do not generate primes.
%e 2//0 - 1 = 20 - 1 = 19 = prime(8), 0 is first term;
%e 3//1 - 2 = 31 - 2 = 29 = prime(10), 1 is 2nd term;
%e 6//4 - 5 = 64 - 5 = 59 = prime(17), 4 is 3rd term.
%t n2ncQ[n_]:=PrimeQ[FromDigits[Join[IntegerDigits[n+2], IntegerDigits[ n]]]- n-1]; Select[Range[0,300],n2ncQ] (* _Harvey P. Dale_, Feb 24 2011 *)
%Y Cf. A000040, A065582, A095995, A173976, A177435.
%K base,easy,nonn
%O 1,3
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 11 2010
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