

A178423


Semiprimes for which dropping any digit gives a prime number.


1



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
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OFFSET

1,1


COMMENTS

This is the 2nd row of the infinite array A[k,n] = nth 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: A280646 A295799 A322124 * A108632 A045096 A227408
Adjacent sequences: A178420 A178421 A178422 * A178424 A178425 A178426


KEYWORD

base,nonn


AUTHOR

Jonathan Vos Post, May 27 2010


STATUS

approved



