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A350101
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Numbers k such that 2*k-1 and 2*k+1 are squarefree semiprimes (A046388).
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2
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1) = 17: 2*17 - 1 = 33 = 3*11 and 2*17 + 1 = 35 = 5*7 are both in A046388.
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MAPLE
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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
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MATHEMATICA
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semiQ[n_] := FactorInteger[n][[;; , 2]] == {1, 1}; Select[Range[400], AllTrue[2*# + {-1, 1}, semiQ] &] (* Amiram Eldar, Dec 14 2021 *)
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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