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

1,1

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).

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 *)

Prog

(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

Crossrefs

Cf. A034302-A034305.

Cf. A010051, A259315.

Sequence in context: A177734 A177055 A186780 * A167459 A066737 A121609

Adjacent sequences: A034301 A034302 A034303 * A034305 A034306 A034307

Keyword

base,nonn,nice

Author

David W. Wilson

Extensions

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

Status

approved