A276169 Primes that remain primes after adding to them their largest missing digit.

2, 29, 59, 149, 191, 269, 359, 449, 479, 491, 569, 593, 599, 719, 911, 929, 1109, 1193, 1229, 1319, 1439, 1559, 1619, 1979, 1987, 2129, 2339, 2459, 2549, 2609, 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

Offset: 1

Author

Zak Seidov and Eric Angelini, Aug 22 2016

Keywords

• nonn
• base

Comments

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.

If n > 2, the largest missing digit must be even, so in particular n contains digit 9. - Robert Israel, Sep 01 2016

Pandigital primes not included. - Zak Seidov, Sep 02 2016

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A116667 (largest missing digit).

Programs

Maple

lmd:= n -> max({$1..9} minus convert(convert(n,base,10),set)):
select(t -> isprime(t) and isprime(t + lmd(t)), [2,seq(i,i=3..10000,2)]); # Robert Israel, Sep 01 2016

Mathematica

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

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