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

1,1

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

Links

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

Example

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

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]]]&]

Prog

(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

Crossrefs

Cf. A116667 (largest missing digit).

Sequence in context: A142969 A281546 A115448 * A107161 A372932 A041097

Adjacent sequences: A276166 A276167 A276168 * A276170 A276171 A276172

Keyword

nonn,base

Author

Zak Seidov and Eric Angelini, Aug 22 2016

Status

approved