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

22, 25, 33, 35, 55, 57, 77, 111, 119, 371, 411, 413, 417, 437, 471, 473, 611, 671, 713, 731, 1037, 1073, 1079, 1379, 1397, 1673, 1739, 1937, 1991, 2571, 2577, 2811, 3113, 3131, 3173, 3317, 4331, 4439, 4499, 4631, 6017, 6431, 6773, 7619, 9977, 12777

Offset: 1

Author

Jonathan Vos Post, May 27 2010

Keywords

• base
• nonn

Comments

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.

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

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, ...}.

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, ...}.

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

Examples

			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).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000040, A001358, A034895, A108632.

Programs

Mathematica

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 *)

Formula

A001358 INTERSECTION A034895.