A079310 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).

1, 2, 3, 4, 6, 11, 13, 19, 21, 22, 26, 27, 28, 31, 36, 38, 41, 42, 51, 53, 54, 55, 59, 62, 64, 68, 71, 73, 75, 80, 82, 88, 91, 95, 96, 100, 101, 102, 106, 110, 111, 117, 118, 120, 121, 125, 132, 135, 139, 142, 146, 148, 150, 152, 173, 182, 190, 193, 202, 216, 221, 222

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

phi(19)=18, (6*18-1, 6*18+1) = (107,109) = (A000040(28), A000040(29)), therefore 19 is a term;
phi(20)=8, (6*8-1, 6*8+1) = (47,49) = (A000040(15), 7*7), therefore 20 is not a term;
phi(21)=12, (6*12-1, 6*12+1) = (71,73) = (A000040(20), A000040(21)), therefore 19 is a term.

Mathematica

tpQ[n_]:=Module[{c=6EulerPhi[n]}, PrimeQ[c-1]&&PrimeQ[c+1]]; Select[ Range[ 300], tpQ] (* Harvey P. Dale, May 11 2011 *)
Select[Range[250], AllTrue[6*EulerPhi[#]+{1, -1}, PrimeQ]&] (* Harvey P. Dale, Oct 12 2023 *)

Crossrefs

Cf. A000010, A001359, A006512, A014574.

Sequence in context: A018297 A050886 A341652 * A116853 A342334 A066615

Adjacent sequences: A079307 A079308 A079309 * A079311 A079312 A079313

Keyword

nonn

Author

Reinhard Zumkeller, Feb 10 2003

Status

approved