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%I #19 Oct 12 2023 13:06:39
%S 1,2,3,4,6,11,13,19,21,22,26,27,28,31,36,38,41,42,51,53,54,55,59,62,
%T 64,68,71,73,75,80,82,88,91,95,96,100,101,102,106,110,111,117,118,120,
%U 121,125,132,135,139,142,146,148,150,152,173,182,190,193,202,216,221,222
%N Numbers k such that (6*phi(k)-1, 6*phi(k)+1) is a twin prime pair, where phi is Euler's totient function (A000010).
%H Ivan Neretin, <a href="/A079310/b079310.txt">Table of n, a(n) for n = 1..10000</a>
%e phi(19)=18, (6*18-1, 6*18+1) = (107,109) = (A000040(28), A000040(29)), therefore 19 is a term;
%e phi(20)=8, (6*8-1, 6*8+1) = (47,49) = (A000040(15), 7*7), therefore 20 is not a term;
%e phi(21)=12, (6*12-1, 6*12+1) = (71,73) = (A000040(20), A000040(21)), therefore 19 is a term.
%t tpQ[n_]:=Module[{c=6EulerPhi[n]},PrimeQ[c-1]&&PrimeQ[c+1]]; Select[ Range[ 300],tpQ] (* _Harvey P. Dale_, May 11 2011 *)
%t Select[Range[250],AllTrue[6*EulerPhi[#]+{1,-1},PrimeQ]&] (* _Harvey P. Dale_, Oct 12 2023 *)
%Y Cf. A000010, A001359, A006512, A014574.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Feb 10 2003
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