A383941 a(0) = 0; for n >= 1, a(n) is the smallest positive integer not already in the sequence that is coprime to both a(n-1) and the sum of all preceding terms.

0, 1, 2, 5, 3, 4, 7, 9, 8, 11, 13, 10, 17, 19, 6, 29, 23, 12, 25, 31, 14, 37, 15, 16, 21, 41, 18, 35, 43, 22, 27, 47, 20, 49, 33, 26, 53, 39, 32, 45, 59, 28, 51, 55, 24, 61, 65, 34, 67, 57, 40, 63, 71, 30, 73, 69, 38, 75, 77, 46, 79, 81, 44, 83, 85, 36, 89, 91, 48

Offset

0,3

Comments

Conjecture: This is a permutation of the nonnegative integers.

Links

Felix Huber, Table of n, a(n) for n = 0..10000

Example

a(3) = 5 because 5 is the smallest positive integer not already in the sequence that is coprime to a(2) = 2 and to a(0) + a(1) + a(2) = 0 + 1 + 2 = 3.

Maple

A383941:=proc(n)
    option remember;
    local a;
    if n=0 then
        [0, 0, [0]]
    else
        for a do
            if not member(a, procname(n-1)[3]) and gcd(procname(n-1)[1], a)=1 and gcd(procname(n-1)[2], a)=1 then
                return [a, procname(n-1)[2]+a, [op(procname(n-1)[3]), a]]
            fi
        od
    fi;
end proc;
seq(A383941(n)[1], n=0..68);

Crossrefs

Cf. A084385, A085229, A093714, A103683, A352588.

Sequence in context: A357047 A105530 A370932 * A245815 A105108 A118460

Adjacent sequences: A383938 A383939 A383940 * A383942 A383943 A383944

Keyword

nonn

Author

Felix Huber, Sep 09 2025

Status

approved