A034304 Nonprime; becomes prime if any digit is deleted (zeros not allowed in the number).

22, 25, 27, 32, 33, 35, 52, 55, 57, 72, 75, 77, 111, 117, 119, 171, 371, 411, 413, 417, 437, 471, 473, 611, 671, 711, 713, 731, 1379, 1397, 1673, 1739, 1937, 1991, 2233, 2277, 2571, 2577, 2811, 3113, 3131, 3173, 3311, 3317, 3479, 4199, 4331, 4433, 4439

Offset: 1

Author

David W. Wilson

Keywords

• base
• nonn
• nice

Comments

From David A. Corneth, Sep 14 2019: (Start)

Terms can't contain digits of the form 0 (mod 3), 1 (mod 3) and 2 (mod 3) as then one can remove a digit to get a multiple of 3. Classifying digits mod 3 could give further restrictions on the frequency of digits per class.

For example, let (d0, d1, d2) be the frequency of digits from each residue class mod 3 respectively. Then a term can't be of the form (0, 2, 3) as removing a digit from the class 2 (mod 3) gives a multiple of 3. (End)

Links

• David A. Corneth, Table of n, a(n) for n = 1..502 (first 200 terms from T. D. Noe, terms n = 201..299 from R. Zumkeller, terms <= 10^11).

Crossrefs

Cf. A034302-A034305.

Cf. A010051, A259315.

Programs

Haskell

a034304 n = a034304_list !! (n-1)
a034304_list = map read $ filter (f "") $
               map show $ dropWhile (< 10) a259315_list :: [Integer] where
   f _ "" = True
   f us (v:vs) = a010051' (read (us ++ vs)) == 1 && f (us ++ [v]) vs
-- Reinhard Zumkeller, Jun 24 2015

Mathematica

With[{nn=5000},Select[Complement[Range[10,nn],Prime[Range[ PrimePi[ nn]]]], DigitCount[#,10,0]==0&&And@@PrimeQ[FromDigits/@Subsets[ IntegerDigits[#],{IntegerLength[#]-1}]]&]] (* Harvey P. Dale, Apr 06 2012 *)

Extensions

Definition corrected by T. D. Noe, Apr 02 2008