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 A178423 Semiprimes for which dropping any digit gives a prime number. 1

%I

%S 22,25,33,35,55,57,77,111,119,371,411,413,417,437,471,473,611,671,713,

%T 731,1037,1073,1079,1379,1397,1673,1739,1937,1991,2571,2577,2811,3113,

%U 3131,3173,3317,4331,4439,4499,4631,6017,6431,6773,7619,9977,12777

%N Semiprimes for which dropping any digit gives a prime number.

%C This is the 2nd row of the infinite array A[k,n] = n-th number with k prime factors (not necessarily distinct) for which dropping any digit gives a prime number.

%C The first row A[1,n] = A051362 = numbers n such that n remains prime if any digit is deleted (zeros allowed).

%C The 3rd row A[3,n] begins {27 = 3^3, 52 = 2^2 * 13, 75 = 3 * 5^2, 117 = 3^2 * 13, 171 = 3^2 * 19, ...}.

%C The 4th row A[4,n] begins: {2277 = 3^2 * 11 * 23, 5577 = 3 * 11 * 13^2, 8211 = 3 * 7 * 17 * 23, 8811 = 3^2 * 11 * 89, ...}.

%C The 5th row A[5,n] begins:{32 = 2^5, 72 = 2^3 x 3^2, ...}.

%H Harvey P. Dale, <a href="/A178423/b178423.txt">Table of n, a(n) for n = 1..100</a>

%F A001358 INTERSECTION A034895.

%e a(9) = 119 because this is a semiprime (119 = 7 * 17), dropping the leftmost digit gives 19 (a prime), dropping the middle digit gives 19 (a prime), and dropping the rightmost digit gives 11 (a prime).

%t ddp[n_]:=Module[{idn=IntegerDigits[n]},PrimeOmega[n]==2 && And@@PrimeQ[ FromDigits/@Table[Drop[idn,{i}],{i,Length[idn]}]]]; Select[Range[ 13000],ddp] (* _Harvey P. Dale_, Apr 10 2012 *)

%Y Cf. A000040, A001358, A034895, A108632.

%K base,nonn

%O 1,1

%A _Jonathan Vos Post_, May 27 2010

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Last modified August 8 14:04 EDT 2020. Contains 336298 sequences. (Running on oeis4.)