A328160 Terms k of A112998 such that k+2 is nonsquarefree.

61, 73, 277, 421, 2797, 6217, 8521, 9277, 9817, 10357, 11161, 12301, 12841, 13381, 15121, 17377, 17881, 18097, 19861, 25657, 30517, 30661, 33037, 35521, 36241, 36457, 48121, 50821, 51481, 54421, 56437, 58417, 60217, 66601, 66697, 67057, 71341, 74077, 77641, 79801, 88117, 94777, 96181, 98017

Offset

1,1

Comments

Complement of A328137 in A112998.

Each term is either 3*x^2-2 where x, 3*x^2-2 and (3*x^2-1)/2 are prime or it is 9*x-2 where x, 9*x-2 and (9*x-1)/2 are prime.

Links

Robert Israel, Table of n, a(n) for n = 1..7487

Example

a(3)=277 is a term because 277 is prime, 277+1=2*139 where 139 is prime, and 279=3^2*31 is a 3-almost prime that is nonsquarefree.

Maple

N:= 100000:
A1:= map(x -> 3*x^2-2, select(x -> isprime(x) and isprime(3*x^2-2) and isprime((3*x^2-1)/2), {seq(i, i=3..floor(sqrt((N+2)/3)), 2)})):
A2:= map(x -> 9*x-2, select(x -> isprime(x) and isprime(9*x-2) and isprime((9*x-1)/2), {seq(i, i=3..(N+2)/9, 2)})):
sort(convert(A1 union A2, list));

Mathematica

Select[Prime@ Range[10^4], And[PrimeOmega /@ {# + 1, # + 2} == {2, 3}, ! SquareFreeQ[# + 2]] &] (* Michael De Vlieger, Oct 06 2019 *)

Crossrefs

Cf. A112998, A328137.

Sequence in context: A141457 A112998 A339778 * A118162 A217076 A281960

Adjacent sequences: A328157 A328158 A328159 * A328161 A328162 A328163

Keyword

nonn

Author

Robert Israel, Oct 05 2019

Status

approved