A359535 -id:A359535 - cp's OEIS frontend

A366170 Lexicographically earliest sequence of distinct positive integers such that for n>1, Sum_{i=1..n, a(i)<=n} a(a(i)) is prime.

1, 2, 4, 8, 6, 12, 5, 7, 10, 18, 13, 11, 14, 16, 17, 24, 20, 22, 21, 15, 19, 26, 3, 23, 9, 30, 28, 32, 31, 29, 40, 42, 34, 36, 37, 44, 35, 27, 41, 50, 46, 39, 33, 56, 47, 52, 68, 49, 43, 54, 53, 51, 60, 58, 57, 45, 66, 55, 61, 74, 64, 63, 84, 72, 67, 78, 65, 59, 70, 90, 73, 80

Offset: 1

Neal Gersh Tolunsky, Oct 02 2023

nonn

At a new term k, a(n) = k adds a(k) to the current prime sum if k <= n. If n is a term in the sequence among a(1..n-1), then a(n) = k is added. If neither of these conditions is met, the current prime sum remains the same.
If k is even and a(k) odd, then k cannot appear as a(n) = k at any n >= k (otherwise, the intended prime sum will be even, and thus not prime). This means that some even numbers will miss their chance and never appear. 38 is the smallest missing number.
Can it be proved that every odd number appears?

			At [1,2], the terms at indices i=1 and i=2, namely 1 and 2, sum to 3, a prime.
At [1,2,4], i=4 is not the index of a term in the sequence yet, so the sum remains the same.
At [1,2,4,8], the sum of the terms at i=1,2,4 is a(1)=1 + a(2)=2 + a(4)=8, which is 11, a prime number.

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
Neal Gersh Tolunsky, Graph of the first differences for n = 1..10001

Cf. A054408, A180405, A359535.

cp's OEIS Frontend

A366170 Lexicographically earliest sequence of distinct positive integers such that for n>1, Sum_{i=1..n, a(i)<=n} a(a(i)) is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs