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

1,1

Links

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

Example

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

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 *)

Prog

(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)

Crossrefs

Cf. A046388.

Intersection of A234093 and A234096.

Sequence in context: A366963 A032611 A255200 * A360972 A319265 A238572

Adjacent sequences: A350098 A350099 A350100 * A350102 A350103 A350104

Keyword

nonn

Author

Hugo Pfoertner, Dec 14 2021

Status

approved