

A354224


Lexicographically earliest sequence of distinct positive integers such that a(1) = 1 and for any n > 1, the greatest common divisor of n and a(n) is a prime number.


0



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

1,2


COMMENTS

This sequence is a selfinverse permutation of the positive integers.


LINKS



FORMULA

a(n) = n iff n = 1 or n is a prime number.


EXAMPLE

The first terms are:
n a(n) gcd(n, a(n))
  
1 1 1
2 2 2
3 3 3
4 6 2
5 5 5
6 4 2
7 7 7
8 10 2
9 12 3
10 8 2
11 11 11
12 9 3
13 13 13
14 16 2


PROG

(PARI) s=0; for (n=1, 67, for (v=1, oo, if (!bittest(s, v) && (n==1  isprime(gcd(n, v))), print1 (v", "); s+=2^v; break)))
(Python)
from math import gcd
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
aset, mink = {1}, 2; yield 1
for n in count(2):
k = mink
while k in aset or not isprime(gcd(n, k)): k += 1
aset.add(k); yield k
while mink in aset: mink += 1


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



