A007597 Strobogrammatic primes.

11, 101, 181, 619, 16091, 18181, 19861, 61819, 116911, 119611, 160091, 169691, 191161, 196961, 686989, 688889, 1008001, 1068901, 1160911, 1180811, 1190611, 1191611, 1681891, 1690691, 1880881, 1881881, 1898681, 1908061, 1960961, 1990661, 6081809, 6100019, 6108019

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

• base
• nonn

Comments

Primes which are invariant under a 180-degree rotation.

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• C. W. Trigg, "Strobogrammatic Primes and Prime Rotative Twins", J. Rec. Math., 15 (1983), 281-282.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..304 from K. D. Bajpai)
• C. K. Caldwell, The Prime Glossary, Strobogrammatic
• Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
• Wikipedia, Strobogrammatic prime

Crossrefs

Cf. A000787.

Programs

Mathematica

lst = {}; fQ[n_] := Block[{allset = {0, 1, 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, 2000000}]; lst (* Robert G. Wilson v, Feb 27 2007 *)

Python

from sympy import isprime
from itertools import count, islice, product
def ud(s): return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
def agen():
    for d in count(2):
        for start in "1689":
            for rest in product("01689", repeat=d//2-1):
                left = start + "".join(rest)
                right = ud(left)
                for mid in [[""], ["0", "1", "8"]][d%2]:
                    t = int(left + mid + right)
                    if isprime(t):
                        yield t
print(list(islice(agen(), 33))) # Michael S. Branicky, Mar 29 2022

Extensions

More terms from David W. Wilson

a(31)-a(33) from K. D. Bajpai, Jun 23 2017