A068853 a(1) = 2; a(n+1) is the smallest prime > a(n) which differs from it in every digit.

2, 3, 5, 7, 11, 23, 31, 43, 59, 61, 73, 89, 97, 101, 223, 307, 419, 503, 617, 701, 823, 907, 1013, 2129, 3001, 4127, 5003, 6121, 7013, 8101, 9013, 10139, 21001, 30113, 41039, 50101, 61027, 70111, 81023, 90107, 101021, 210109, 301013, 410141, 501013, 610157, 701009

Offset: 1

Author

Amarnath Murthy, Mar 12 2002

Keywords

• base
• nonn

Comments

a(8996) has 1001 digits. - Michael S. Branicky, Mar 19 2024

Examples

			223 is a member and the next few primes are 227, 229, ... 283, 297, 307. 307 is the smallest one which differs from 223 in all corresponding positions.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..8995

Crossrefs

Cf. A068863.

Programs

Python

from sympy import isprime
from itertools import count, islice, product
def diffgen(n): # generator of numbers >n sharing no digits with n
    s = str(n)
    P = [list(str(d) for d in range(10) if str(d) != si) for si in s]
    if s[0] < '9':
        f = [d for d in P[0] if d > s[0]]
        for t in product(*([f]+P[1:])):
            yield int("".join(t))
    for e in count(1):
        for t in product("123456789", *(["0123456789"]*(e-1) + P)):
            yield int("".join(t))
def agen(): # generator of terms
    an = 2
    while True:
        yield an
        an = next(k for k in diffgen(an) if isprime(k))
print(list(islice(agen(), 47))) # Michael S. Branicky, Mar 19 2024

Extensions

Corrected and extended by Ray Chandler, Jul 19 2003

a(46) and beyond from Michael S. Branicky, Mar 19 2024