A034304 - OEIS

%I #34 Sep 27 2019 02:53:37

%S 22,25,27,32,33,35,52,55,57,72,75,77,111,117,119,171,371,411,413,417,

%T 437,471,473,611,671,711,713,731,1379,1397,1673,1739,1937,1991,2233,

%U 2277,2571,2577,2811,3113,3131,3173,3311,3317,3479,4199,4331,4433,4439

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

%C From _David A. Corneth_, Sep 14 2019: (Start)

%C 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.

%C 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)

%H David A. Corneth, <a href="/A034304/b034304.txt">Table of n, a(n) for n = 1..502</a> (first 200 terms from T. D. Noe, terms n = 201..299 from R. Zumkeller, terms <= 10^11).

%t 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 *)

%o (Haskell)

%o a034304 n = a034304_list !! (n-1)

%o a034304_list = map read $ filter (f "") $

%o                map show $ dropWhile (< 10) a259315_list :: [Integer] where

%o    f _ "" = True

%o    f us (v:vs) = a010051' (read (us ++ vs)) == 1 && f (us ++ [v]) vs

%o -- _Reinhard Zumkeller_, Jun 24 2015

%Y Cf. A034302-A034305.

%Y Cf. A010051, A259315.

%K base,nonn,nice

%O 1,1

%A _David W. Wilson_

%E Definition corrected by _T. D. Noe_, Apr 02 2008