A180561 Primes that cannot become a different prime under any mapping of some single decimal digit <=> with some other single decimal digit.

11, 11779, 22669, 23333, 33533, 55333, 74279, 77999, 78857, 80603, 84871, 88177, 88747, 97039, 103091, 112181, 119701, 125813, 128147, 131143, 133499, 141587, 158771, 159979, 164341, 166063, 173933, 175781, 219613, 220279, 222601, 227387, 229727, 231317, 238829

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Index to Primes, Primes that become a different prime under some mapping.

Formula

Complement of all the primes with the union of the sequences A175791, A175789, A180517 thru A180559.

Mathematica

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, s[[1]]] || MemberQ[id, s[[2]]]) && PrimeQ[ FromDigits[id /. {s[[1]] -> s[[2]], s[[2]] -> s[[1]] }] ]]; t = Union@ Flatten@ Table[s = {j, k}; Select[ Prime@ Range@ 25000, fQ], {j, 0, 8}, {k, j + 1, 9}] ]]; Complement[ Prime@ Range@ 25000, t]

Prog

(Python)
from sympy import isprime
def m(s):
    return [s.translate({ord(c):ord(d), ord(d):ord(c)}) for c in set(s) for d in "0123456789" if d != c]
def ok(n):
    return isprime(n) and not any(isprime(int(t)) for t in m(str(n)))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Oct 31 2023

Crossrefs

Cf. A175791, A180517 thru A180559, A175789, A180560.

Sequence in context: A228566 A228533 A088103 * A185538 A125545 A068137

Adjacent sequences: A180558 A180559 A180560 * A180562 A180563 A180564

Keyword

base,nonn

Author

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Extensions

a(33) and beyond from Michael S. Branicky, Oct 31 2023

Status

approved