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A328160 Terms k of A112998 such that k+2 is nonsquarefree. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..44.

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: A260808 A141457 A112998 * A118162 A217076 A281960

Adjacent sequences:  A328157 A328158 A328159 * A328161 A328162 A328163

KEYWORD

nonn

AUTHOR

Robert Israel, Oct 05 2019

STATUS

approved

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Last modified January 22 13:41 EST 2020. Contains 331149 sequences. (Running on oeis4.)