A289123 Numbers n such that (n-2,n) are twin primes, and (n,n+2) are twin lucky numbers.

7, 13, 31, 73, 193, 283, 619, 643, 883, 1021, 1093, 1231, 2083, 2113, 2971, 3121, 3259, 4129, 4483, 4519, 5233, 6271, 6661, 6763, 7549, 7591, 8221, 9421, 10069, 10459, 10531, 11833, 12163, 13009, 13693, 13723, 13831, 17209, 17389, 20149, 20509, 21013, 21613

Offset: 1

Author

Amiram Eldar, Jun 25 2017

Keywords

• nonn

Comments

Intersection of A006512 and A031158. Subsequence of A031157. The other case in which (n-2,n) are twin lucky numbers, and (n,n+2) are twin primes has only one solution, n = 3, since twin primes are of the form (6k-1, 6k+1) (except for 3 and 5) and 6k-1 is never lucky.

Examples

			7 is in the sequence since (5,7) are twin primes, and (7,9) are twin lucky numbers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006512, A000959, A031157, A031158.

Programs

Mathematica

L = Table[2*i + 1, {i, 0, 10^5}]; For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]]; L[[Select[Range[1, Length[L] - 1], PrimeQ[L[[#]] - 2] && PrimeQ [L[[#]]] && L[[# + 1]] == L[[#]] + 2 &]]] (* after Jean-François Alcover at A000959 *)