A317179 Palindromic invertible primes.

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

Offset: 1

Author

K. D. Bajpai, Jul 23 2018

Keywords

• nonn
• base

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

Examples

			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.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..15175
• C. K. Caldwell, The Prime Glossary, strobogrammatic
• Wikipedia, Strobogrammatic number

Crossrefs

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

Programs

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[#]]]  &]

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