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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. 5
 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, 1108201, 1108501, 1110881, 1120121, 1120211 (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 *) PROG (Python) from sympy import isprime from itertools import count, islice, product def t(s): return s.translate({ord("2"):ord("5"), ord("5"):ord("2")}) def ok(s): # s is a string of digits return all(isprime(int(w)) for w in [s, s[::-1], t(s), t(s[::-1])]) def agen(): # generator of terms yield from (2, 5) for d in count(2): for mid in product("01258", repeat=d-2): s = "1" + "".join(mid) + "1" if ok(s): yield int(s) print(list(islice(agen(), 35))) # Michael S. Branicky, Apr 27 2024 CROSSREFS Cf. A134997, A134998, A048661. Sequence in context: A309375 A018847 A178318 * A134998 A078790 A158999 Adjacent sequences: A134993 A134994 A134995 * A134997 A134998 A134999 KEYWORD nonn,base,nice AUTHOR Mike Keith EXTENSIONS 5 added by Patrick Capelle, Feb 06 2008 STATUS approved

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Last modified August 13 22:54 EDT 2024. Contains 375146 sequences. (Running on oeis4.)