A362962 - OEIS

A362962

Lexicographically earliest sequence of distinct positive terms such that if a(n) jumps over a(n) positions towards the right (landing on the integer k), the sum a(n) + k is always prime.

1, 2, 4, 5, 3, 6, 7, 9, 10, 8, 11, 12, 13, 14, 16, 17, 15, 20, 21, 19, 22, 23, 18, 24, 25, 26, 28, 29, 27, 30, 31, 37, 32, 36, 33, 34, 35, 38, 39, 40, 46, 41, 42, 45, 43, 44, 47, 48, 49, 50, 54, 51, 53, 55, 52, 61, 56, 60, 57, 58, 59, 62, 66, 63, 64, 65, 67, 68

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OFFSET

1,2

COMMENTS

a(n) - a(n+k) = k with k odd is forbidden as this would lead to a contradiction. This is why a(4) = 5 here and not a(4) = 3.

The sequence is a permutation of the natural numbers.

LINKS

Table of n, a(n) for n=1..68.

EXAMPLE

S = 1, 2, 4, 5, 3, 6, 7, 9, 10, 8, 11, 12, 13, ...

sum = 5 5 13 13 13 19

a(1) = 1 and 1 + 4 = 5 (prime)