A168612 In binary starting with 1, prepend a 1 and as few 0's as required such that the new number is relatively prime to all previous in sequence. Thus binary 1, 11, 111, 10111, 110111, 100110111, 1100110111, 11100110111.

1, 3, 7, 23, 55, 311, 823, 1847, 10039, 26423, 8415031, 25192247, 58746679, 1132488503, 3279972151, 7574939447, 16164874039, 291042780983, 840798594871, 1940310222647, 4139333478199, 74508077655863, 215245566011191, 496720542721847, 1059670496143159

Offset

1,2

Comments

a(169) has 1003 digits. - Michael S. Branicky, Feb 07 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..168

Wikipedia, Mathematics reference desk 2009 December 1. Sequence proposed by Julzes.

Mathematica

f[s_] := Append[s, i = 0; While[! AllTrue[s, CoprimeQ[2^(i+BitLength[Last[s]])+Last[s], #] &], i++]; 2^(i+BitLength[Last[s]])+Last[s]];
Nest[f, {1}, 30] (* Seth A. Troisi, Feb 07 2023 *)

Prog

(Python)
from math import gcd
from itertools import count, islice
def agen(): # generator of terms
    an, alst = 1, []
    while True:
        yield an; alst.append(an); b = an.bit_length(); t = 1 << b
        for z in count(0):
            an = (t << z) + alst[-1]
            if all(gcd(an, ai) == 1 for ai in alst): break
print(list(islice(agen(), 25))) # Michael S. Branicky, Feb 07 2023

Crossrefs

Cf. A171134.

Sequence in context: A219167 A293466 A231722 * A332866 A127178 A001275

Adjacent sequences: A168609 A168610 A168611 * A168613 A168614 A168615

Keyword

nonn,base

Author

Steve Bailey (SGBailey(AT)iee.org), Dec 01 2009

Extensions

a(9)-a(23) from James G. Merickel and John W. Layman, Dec 03 2009

a(24)-a(25) from Alois P. Heinz, Feb 07 2023

Status

approved