A068803 Smaller of two consecutive primes which have no common digits.

2, 3, 5, 7, 19, 29, 37, 47, 59, 79, 97, 397, 499, 599, 1999, 2999, 3989, 4999, 29989, 49999, 59999, 79999, 199999, 599999, 799999, 2999999, 4999999, 5999993, 19999999, 29999999, 59999999, 69999989, 99999989, 199999991, 699999953, 799999999, 5999999989, 6999999989

Offset

1,1

Comments

Is the sequence finite or infinite?

Except for 2, 3, 5, and 7, all such primes are of the form a*10^n-b with 1 <= a <= 8 and b mod 10 = 1, 3, 7 or 9. An example of a large pair is 10^101-203 and 10^101+3. The largest known pair of probable primes is 8*10^5002-6243 and 8*10^5002+14481. - Lewis Baxter, Mar 06 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..804

Example

397 is a term as 397 and 401 are two consecutive primes with no common digits.

Mathematica

First /@ Select[Partition[Prime[Range[10^6]], 2, 1], Intersection @@ IntegerDigits /@ # == {} &] (* Jayanta Basu, Aug 06 2013 *)

Prog

(PARI) isok(p) = isprime(p) && (#setintersect(Set(digits(p)), Set(digits(nextprime(p+1)))) == 0); \\ Michel Marcus, Mar 27 2023
(Python)
from itertools import count, islice
from sympy import nextprime, prevprime
def agen(): # generator of terms
    yield from [2, 3, 5]
    for d in count(2):
        for b in range(10**(d-1), 10**d, 10**(d-1)):
            p, q = prevprime(b), nextprime(b)
            if set(str(p)) & set(str(q)) == set():
                yield p
print(list(islice(agen(), 40))) # Michael S. Branicky, May 09 2023

Crossrefs

Cf. A076490.

Sequence in context: A346167 A163074 A230041 * A184902 A048419 A087562

Adjacent sequences: A068800 A068801 A068802 * A068804 A068805 A068806

Keyword

base,nonn

Author

Amarnath Murthy, Mar 06 2002

Extensions

More terms from Larry Soule (lsoule(AT)gmail.com), Jun 21 2006

a(36) and beyond from Michael S. Branicky, May 09 2023

Status

approved