A317029 Invertible primes p such that k*p - 1 and k*p + 1 is a twin prime pair; for k = 12.

19, 601, 1601, 16661, 16981, 19609, 60689, 66809, 69001, 69011, 100169, 119191, 189901, 196919, 616961, 1061689, 1088089, 1091119, 1106069, 1196089, 1198069, 1611601, 1666019, 1688969, 1800119, 1861889, 1891619, 1891661, 1910669, 1996681, 6060091, 6160601, 6196909

Offset

1,1

Comments

Intersection of A048890 (invertible primes) and A138242.

k = 12 is the smallest integer to produce such sequence.

Links

Table of n, a(n) for n=1..33.

Example

a(2) = 601 is an invertible prime; 12*601 - 1 = 7211; 12*601 + 1 = 7213; 7211 and 7213 form a twin prime pair.
a(4) = 16661 is an invertible prime; 12*16661 - 1 = 199931; 12*16661 + 1 = 199933; 199931 and 199933 form a twin prime pair.

Mathematica

k = 12; Select[lst = {};
fQ[n_] := Block[{allset = {0, 1, 6, 8, 9}, id = IntegerDigits@n}, rid = Reverse[id /. {6 -> 9, 9 -> 6}]; Union@Join[id, allset] == allset && PrimeQ@FromDigits@rid && rid != id]; Do[If[PrimeQ@n && fQ@n, AppendTo[lst, n]], {n, 12000000}]; lst,
PrimeQ[k# + 1] && PrimeQ[k# - 1] &]

Crossrefs

Cf. A048890, A001359, A006512, A124519, A138242.

Sequence in context: A226584 A180841 A266052 * A183516 A290007 A119555

Adjacent sequences: A317026 A317027 A317028 * A317030 A317031 A317032

Keyword

nonn,base

Author

K. D. Bajpai, Jul 19 2018

Status

approved