A018847 Strobogrammatic primes: the same upside down (calculator-style numerals).

2, 5, 11, 101, 151, 181, 619, 659, 6229, 10501, 12821, 15551, 16091, 18181, 19861, 60209, 60509, 61519, 61819, 62129, 116911, 119611, 160091, 169691, 191161, 196961, 605509, 620029, 625529, 626929, 650059, 655559, 656959, 682289, 686989, 688889

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Comments

This is the subsequence of primes in A018846. - M. F. Hasler, May 05 2012

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..648 from M. F. Hasler)

Crossrefs

Cf. A007597 (more restrictive version not allowing digits 2 or 5).

Programs

Mathematica

lst = {}; fQ[n_] := Block[{allset = {0, 1, 2, 5, 6, 8, 9}, id = IntegerDigits@n}, Union@ Join[id, allset] == allset && Reverse[id /. {6 -> 9, 9 -> 6}] == id]; Do[ If[ PrimeQ@n && fQ@n, AppendTo[lst, n]], {n, 700000}]; lst (* Robert G. Wilson v, Feb 27 2007 *)

PARI

{write("/tmp/b018847.txt","1 2\n2 5"); c=2; s2=[0,1,2,5,6,8,9]; s=[0,1,2,5,8]; s1=[0,1,2,5,9,8,6]; for(n=2,9, p1=vector( (n+1)\2, i, 10^(i-1)); p2=vector( (n+1)\2, i, 10^(n-i)); forvec( v=vector((n+1)\2,i,if( i>1, [ 1,if( i>n\2, #s, #s1)], [2,5])), v[1]==3 & v[1]=5; ispseudoprime( t=sum(i=1,n\2,p1[i]*s1[v[i]]+p2[i]*s2[v[i]] ) +if(n%2,p1[#p1]*s[v[#v]] )) & /* print1(t",") */ write("/tmp/b018847.txt",c++" "t)))} \\ - M. F. Hasler, Apr 26 2012

PARI

is_A018847(n,t=Vec("012..59.86"))={ isprime(n) & apply(x->t[eval(x)+1], n=Vec(Str(n)))==vecextract(n, "-1..1") } \\ - M. F. Hasler, May 05 2012

Python

from itertools import count, islice
from sympy import isprime
def A018847_gen(): # generator of terms
    r, t, u = ''.maketrans('69','96'), set('0125689'), {0,1,2,5,8}
    for x in count(1):
        for y in range(10**(x-1),10**x):
            if y%10 in u:
                s = str(y)
                if set(s) <= t and isprime(m:=int(s+s[-2::-1].translate(r))):
                    yield m
        for y in range(10**(x-1),10**x):
            s = str(y)
            if set(s) <= t and isprime(m:=int(s+s[::-1].translate(r))):
                yield m
A018847_list = list(islice(A018847_gen(),20)) # Chai Wah Wu, Apr 09 2024