A256386 Numbers m such that m-2, m-1, m+1, m+2 cannot all be represented in the form x*y + x + y for values x, y with x >= y > 1.

2, 3, 4, 5, 8, 11, 59, 1319, 1619, 4259, 5099, 6659, 6779, 11699, 12539, 21059, 66359, 83219, 88259, 107099, 110879, 114659, 127679, 130199, 140759, 141959, 144539, 148199, 149519, 157559, 161339, 163859, 175079, 186479, 204599, 230939, 249539, 267959, 273899, 312839

Offset: 1

Author

Alex Ratushnyak, Mar 31 2015

Keywords

• nonn

Comments

Indices of terms surrounded by pairs of zeros in A255361.

Conjectures:

1. A255361(a(n)) > 0 for n > 4.

2. All terms > 8 are primes.

3. All terms > 8 are terms of these supersequences: A118072, A171667, A176821, A181602, A181669.

From Lamine Ngom, Feb 12 2022: (Start)

For n > 4, a(n) is not a term of A254636. This means that a(n)-2, a(n)-1, a(n)+1 and a(n)+2 are adjacent terms in A254636.

Number of terms < 10^k: 5, 7, 7, 13, 19, 96, 441, 2552, ...

Conjecture 2 would follow if we establish the equivalence "t is in sequence" <=> "t is a term of b(n): lesser of twin primes pair p and q such that (p - 1)/2 and (q + 1)/2 are also a pair of twin primes (A077800)".

It appears that b(n) = a(n) for n > 5. Verified for all terms < 10^9. (End)

Examples

			9, 10, 12, 13 cannot be represented as x*y + x + y, where x >= y > 1. Therefore 11 is in the sequence.
		

Crossrefs

Cf. A255361, A254636.

Cf. A118072, A171667, A176821, A181602, A181669.

Cf. A001097, A001359, A006512, A077800, A158870.

Formula

a(n) = A158870(n-5) - 2, n > 5 (conjectured). - Lamine Ngom, Feb 12 2022