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

1,1

Comments

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

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A068863.

Sequence in context: A019344 A229291 A057459 * A328076 A236400 A288371

Adjacent sequences: A068850 A068851 A068852 * A068854 A068855 A068856

Keyword

base,nonn

Author

Amarnath Murthy, Mar 12 2002

Extensions

Corrected and extended by Ray Chandler, Jul 19 2003

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

Status

approved