A353780 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that is coprime to a(n-1), does not equal a(n-1)+1, and has no digit in common with a(n-1).

1, 3, 2, 5, 4, 7, 6, 11, 8, 13, 9, 14, 23, 10, 27, 16, 25, 17, 20, 19, 22, 15, 26, 31, 24, 35, 12, 37, 18, 29, 33, 28, 39, 41, 30, 47, 21, 34, 55, 32, 45, 38, 49, 36, 59, 40, 51, 43, 50, 61, 42, 53, 44, 57, 46, 71, 48, 65, 72, 83, 52, 63, 58, 67, 54, 73, 56, 79, 60, 77, 62, 75, 64, 81, 70

Offset: 1

Author

Scott R. Shannon, May 07 2022

Keywords

• nonn
• base

Comments

The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(15) = 27 as a(14) = 10, and 27 has not yet appeared, is coprime to 10, is not 1 more than 10, and has no digit in common with 10. Note that 21 satisfies all of these conditions except the last. This is the first term to differ from A353904.
		

Links

• Scott R. Shannon, Image of the first 75000 terms. The green line is y = n.

Crossrefs

Cf. A353904, A093714, A068861, A109812.

Programs

Python

from math import gcd
from itertools import islice
def c(san, k): return set(san) & set(str(k)) == set()
def agen(): # generator of terms
    an, aset, mink = 1, {1}, 2
    while True:
        yield an
        k, san = mink, str(an)
        while k in aset or gcd(an, k) != 1 or k-an == 1 or not c(san, k):
            k += 1
        an = k
        aset.add(an)
        while mink in aset: mink += 1
print(list(islice(agen(), 75))) # Michael S. Branicky, May 23 2022