A276169 - OEIS

%I #20 Sep 03 2016 23:56:47

%S 2,29,59,149,191,269,359,449,479,491,569,593,599,719,911,929,1109,

%T 1193,1229,1319,1439,1559,1619,1979,1987,2129,2339,2459,2549,2609,

%U 2699,2897,2909,2963,3209,3299,3449,3491,3539,3719,3911,3923,4019,4049,4091,4349,4649,4793,4943,4987,5099,5399,5519,5639,5693,5897

%N Primes that remain primes after adding to them their largest missing digit.

%C Resulting primes are: 11, 37, 67, 157, 199, 277, 367, 457, 487, 499, 577, 601, 607, 727, 919, 937, 1117, 1201, 1237, 1327, 1447, 1567, 1627, 1987, 1993, 2137.

%C If n > 2, the largest missing digit must be even, so in particular n contains digit 9. - _Robert Israel_, Sep 01 2016

%C Pandigital primes not included. - _Zak Seidov_, Sep 02 2016

%H Robert Israel, <a href="/A276169/b276169.txt">Table of n, a(n) for n = 1..10000</a>

%e 2+9=11, 29+8=37, 59+8=67 all primes.

%p lmd:= n -> max({$1..9} minus convert(convert(n,base,10),set)):

%p select(t -> isprime(t) and isprime(t + lmd(t)), [2,seq(i,i=3..10000,2)]); # _Robert Israel_, Sep 01 2016

%t Select[Prime[Range[1000]],PrimeQ[#+Complement[Range[9],IntegerDigits[#]][[-1]]]&]

%o (PARI) is(n) = {my(s); if(isprime(n), s = setminus(s=Set(vector(9, i, i)), Set(digits(n))); if(#s>0, n+=s[#s], return(0)); return(isprime(n)))} \\ _David A. Corneth_, Aug 23 2016

%Y Cf. A116667 (largest missing digit).

%K nonn,base

%O 1,1

%A _Zak Seidov_ and _Eric Angelini_, Aug 22 2016