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A177212
Numbers k that are the products of two distinct primes such that 2*k-1, 4*k-3 and 8*k-7 are also products of two distinct primes.
10
247, 249, 295, 395, 422, 478, 493, 502, 519, 589, 634, 694, 721, 755, 955, 1255, 1267, 1294, 1306, 1351, 1387, 1441, 1522, 1546, 1727, 1762, 1942, 2031, 2119, 2155, 2323, 2374, 2449, 2491, 2509, 2533, 2587, 2623, 2661, 2733, 2773, 3005, 3039, 3091, 3334
OFFSET
1,1
LINKS
EXAMPLE
247 is a term because 247 = 13*19, 2*247 - 1 = 493 = 17*29, 4*247-3 = 985 = 5*197, and 8*247 - 1 = 1969 = 11*179.
MAPLE
isA006881:= proc(n) local F;
F:= ifactors(n)[2];
nops(F)=2 and F[1, 2]+F[2, 2]=2
end proc:
filter:= n -> andmap(isA006881, [n, 2*n-1, 4*n-3, 8*n-7]);
select(filter, [$1..10000]); # Robert Israel, Jul 11 2017
MATHEMATICA
f[n_]:=Last/@FactorInteger[n]=={1, 1}; lst={}; Do[If[f[n]&&f[2*n-1]&&f[4*n-3]&&f[8*n-7], AppendTo[lst, n]], {n, 0, 3*7!}]; lst
p2dpQ[n_]:=Transpose[FactorInteger[n]][[2]]=={1, 1}; With[{s=Select[Range[ 3500], p2dpQ]}, Select[s, AllTrue[{2#-1, 4#-3, 8#-7}, p2dpQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 27 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved