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A134996 Dihedral calculator primes: p, p upside down, p in a mirror, p upside-down-and-in-a-mirror are all primes. 4
2, 5, 11, 101, 181, 1181, 1811, 18181, 108881, 110881, 118081, 120121, 121021, 121151, 150151, 151051, 151121, 180181, 180811, 181081, 188011, 188801, 1008001, 1022201, 1028011, 1055501, 1058011, 1082801, 1085801, 1088081 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The digits of a(n) are restricted to 0, 1, 2, 5, 8. - Ivan N. Ianakiev, Oct 08 2015

The first term containing all the possible digits is 108225151. There are 2958 such terms up to 10^12, the last one in this range being 188885250551. - Giovanni Resta, Oct 08 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..7174

C. K. Caldwell, The Prime Glossary, Dihedral Prime

Eric Weisstein's World of Mathematics, Dihedral Prime.

EXAMPLE

120121 is such a number because 120121, 121021 (upside down), 151051 (mirror) and 150151 are all prime. (This is the smallest one in which all four numbers are distinct.)

MATHEMATICA

lst1={2, 5};

startQ[n_]:=First[IntegerDigits[n]]==1;

subQ[n_]:=Module[{lst={0, 1, 2, 5, 8}}, SubsetQ[lst, Union[IntegerDigits[n]]]];

rev[n_]:=Reverse[IntegerDigits[n]];

updown[n_]:=FromDigits[rev[n]];

mirror[n_]:=FromDigits[rev[n]/.{2-> 5, 5-> 2}];

updownmirror[n_]:=FromDigits[rev[mirror[n]]];

lst2=Select[Range@188801, And[startQ[#], subQ[#], PrimeQ[#], PrimeQ[updown[#]], PrimeQ[mirror[#]], PrimeQ[updownmirror[#]]]&];

Join[lst1, lst2] (* Ivan N. Ianakiev, Oct 08 2015 *)

CROSSREFS

Cf. A038136, A048660, A048662.

Sequence in context: A267527 A018847 A178318 * A134998 A078790 A158999

Adjacent sequences:  A134993 A134994 A134995 * A134997 A134998 A134999

KEYWORD

nonn,base,nice

AUTHOR

Mike Keith (domnei(AT)aol.com)

EXTENSIONS

5 added by Patrick Capelle, Feb 06 2008

STATUS

approved

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Last modified December 2 13:12 EST 2016. Contains 278678 sequences.