A350101 Numbers k such that 2*k-1 and 2*k+1 are squarefree semiprimes (A046388).

17, 28, 43, 46, 47, 71, 72, 80, 92, 93, 101, 102, 107, 108, 109, 110, 118, 124, 133, 150, 151, 152, 160, 161, 164, 170, 196, 197, 206, 207, 208, 223, 226, 235, 236, 258, 259, 267, 268, 272, 276, 290, 291, 295, 317, 334, 335, 340, 343, 344, 348, 349, 361, 377, 390

Offset: 1

Author

Hugo Pfoertner, Dec 14 2021

Keywords

• nonn

Examples

			a(1) = 17: 2*17 - 1 = 33 = 3*11 and 2*17 + 1 = 35 = 5*7 are both in A046388.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046388.

Intersection of A234093 and A234096.

Programs

Maple

N:= 1000: # for terms <= N
P:= select(isprime,[seq(i,i=3..2*N/3,2)]):
S:= NULL:
for i from 1 to nops(P) do
  for j from 1 to i-1 while P[i]*P[j] <= 2*N+1 do S:= S,P[i]*P[j] od
od:
S:= {S}:
T:= S intersect map(`-`,S,2):
sort(convert(map(t -> (t+1)/2, T),list)); # Robert Israel, Nov 11 2022

Mathematica

semiQ[n_] := FactorInteger[n][[;; , 2]] == {1, 1}; Select[Range[400], AllTrue[2*# + {-1, 1}, semiQ] &] (* Amiram Eldar, Dec 14 2021 *)

PARI

a350101(limit) = {my(sp(k)=omega(k)==2&&bigomega(k)==2);forstep(k=2,2*limit,2, if(sp(k-1)&&sp(k+1),print1(k/2,", ")))};
a350101(390)