A333111 a(n) is the least positive integer not used earlier such that n+1 and the sum of terms up to a(n) are coprime.

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

Offset

1,2

Comments

Conjectured to be a permutation of the positive integers.

Links

Table of n, a(n) for n=1..66.

Example

We start with a(1) = 1. To find a(2), we need the earliest positive integer such that a(1) + a(2) is coprime to 3. So, a(2) = 3. To find a(3), we can use neither 2 nor 4, because 6 and 8 have a common factor with 4, so we use a(3) = 5.

Prog

(PARI) A333111_vec(N, a=Vec(1, N), s=1, u=1)={ for(n=2, N, u+=1<<a[n-1]; for(k=valuation(u+1, 2), oo, bittest(u, k) || gcd(s+k, n+1)>1 || [s+=a[n]=k, break])); a}

Crossrefs

Sequence in context: A372143 A302793 A010782 * A139584 A064790 A113966

Adjacent sequences: A333108 A333109 A333110 * A333112 A333113 A333114

Keyword

nonn

Author

Ali Sada and M. F. Hasler, Mar 07 2020

Status

approved