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

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)
a(2) = 2 and 2 + 3 = 5 (prime)
a(3) = 4 and 4 + 9 = 13 (prime)
a(4) = 5 and 5 + 8 = 13 (prime)
a(5) = 3 and 3 + 10 = 13 (prime)
a(6) = 6 and 6 + 13 = 19 (prime), etc.

Crossrefs

Cf. A182115, A230086.

Sequence in context: A332017 A276127 A182115 * A065182 A060120 A065183

Adjacent sequences: A362959 A362960 A362961 * A362963 A362964 A362965

Keyword

nonn

Author

Eric Angelini, May 10 2023

Extensions

a(22) and beyond from Michael S. Branicky, May 10 2023

Status

approved