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

1,1

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, ...}.

Links

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

Formula

A001358 INTERSECTION A034895.

Example

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).

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 *)

Crossrefs

Cf. A000040, A001358, A034895, A108632.

Sequence in context: A295799 A338603 A322124 * A108632 A045096 A227408

Adjacent sequences: A178420 A178421 A178422 * A178424 A178425 A178426

Keyword

base,nonn

Author

Jonathan Vos Post, May 27 2010

Status

approved