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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A006512, A000959, A031157, A031158.

Sequence in context: A129781 A174217 A040061 * A342691 A215932 A091432

Adjacent sequences: A289120 A289121 A289122 * A289124 A289125 A289126

Keyword

nonn

Author

Amiram Eldar, Jun 25 2017

Status

approved