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A317179 Palindromic invertible primes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

Intersection of A002385 and A048890, or, respectively, A002113 and A048890. - Felix Fröhlich, Jul 24 2018

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..15175

C. K. Caldwell, The Prime Glossary, strobogrammatic

Wikipedia, Strobogrammatic number

EXAMPLE

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.

MATHEMATICA

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[#]]]  &]

PROG

(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

CROSSREFS

Cf. A000040, A002113, A002385, A045574, A048890.

Sequence in context: A170788 A057329 A232450 * A196023 A108843 A232449

Adjacent sequences:  A317176 A317177 A317178 * A317180 A317181 A317182

KEYWORD

nonn,base

AUTHOR

K. D. Bajpai, Jul 23 2018

STATUS

approved

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Last modified May 14 19:50 EDT 2021. Contains 343902 sequences. (Running on oeis4.)