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

1,2

Comments

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

Links

Table of n, a(n) for n=1..75.

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

Example

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.

Prog

(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

Crossrefs

Cf. A353904, A093714, A068861, A109812.

Sequence in context: A085229 A093714 A353904 * A080261 A138310 A270197

Adjacent sequences: A353777 A353778 A353779 * A353781 A353782 A353783

Keyword

nonn,base

Author

Scott R. Shannon, May 07 2022

Status

approved