A353904 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 differs from a(n-1) at every digit.

1, 3, 2, 5, 4, 7, 6, 11, 8, 13, 9, 14, 23, 10, 21, 16, 25, 12, 29, 15, 22, 17, 20, 19, 24, 31, 18, 35, 26, 33, 28, 37, 40, 27, 32, 41, 30, 43, 34, 45, 38, 47, 36, 49, 51, 44, 39, 46, 53, 42, 55, 48, 59, 61, 50, 63, 52, 67, 54, 65, 56, 69, 58, 71, 57, 62, 73, 60, 77, 64, 75, 68, 79, 66, 83, 70, 81

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..77.

Scott R. Shannon, Image of the first 100000 terms. The green line is y = n.

Example

a(13) = 23 as a(12) = 14, and 23 has not yet appeared, is coprime to 14, is not 1 more than 14, and differs at every digit from 14. Note that 17 satisfies all of these conditions except the last. This is the first term to differ from A093714.

Prog

(Python)
from math import gcd
from itertools import islice
def c(san, k):
    sk = str(k)
    return all(sk[-1-i]!=san[-1-i] for i in range(min(len(san), len(sk))))
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(), 77))) # Michael S. Branicky, May 23 2022

Crossrefs

Cf. A353780, A093714, A068861, A109812.

Sequence in context: A277911 A085229 A093714 * A353780 A080261 A138310

Adjacent sequences: A353901 A353902 A353903 * A353905 A353906 A353907

Keyword

nonn,base

Author

Scott R. Shannon, May 10 2022

Status

approved