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A317179
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Palindromic invertible primes.
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1
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16661, 19991, 1160611, 1190911, 1688861, 1988891, 101616101, 101919101, 106111601, 106191601, 109111901, 109161901, 116010611, 116696611, 119010911, 119969911, 160080061, 160101061, 166080661, 169060961, 188868881, 188898881, 190080091, 190101091, 196090691, 199080991
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OFFSET
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1,1
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COMMENTS
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a(38) = 10886968801 is the first term that uses all of the invertible digits (0, 1, 6, 8, 9).
Number of terms < 10^(2k-1): 0, 0, 2, 6, 26, 78, 314, 1010, 3976, 15174, ..., . - Robert G. Wilson v, Jul 24 2018
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LINKS
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EXAMPLE
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16661 is a term because it is a prime and a palindrome as well; when rotated by 180 degrees it becomes 19991 that is also a prime.
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MATHEMATICA
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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, 1090000000}]; lst, # ==FromDigits[Reverse[IntegerDigits[#]]] &]
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PROG
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(PARI) is_palandinv(n) = my(d=digits(n), ineligible_d=[2, 3, 4, 5, 7]); d==Vecrev(d) && #setintersect(vecsort(d), ineligible_d)==0
invert(n) = my(d=digits(n), e=[]); for(k=1, #d, if(d[k]==0, e=concat(e, [0])); if(d[k]==1, e=concat(e, [1])); if(d[k]==6, e=concat(e, [9])); if(d[k]==8, e=concat(e, [8])); if(d[k]==9, e=concat(e, [6]))); subst(Pol(e), x, 10)
is(n) = my(d=digits(n)); is_palandinv(n) && n!=invert(n) && ispseudoprime(invert(n))
forprime(p=1, 2e8, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Jul 24 2018
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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