A345343 Numbers that yield a prime when any single digit is replaced by its digital complement.

3, 5, 7, 8, 17, 33, 39, 47, 63, 71, 77, 93, 107, 171, 177, 221, 223, 287, 333, 339, 401, 441, 447, 699, 823, 827, 857, 883, 999, 1421, 1781, 2087, 2089, 2171, 2233, 2539, 3253, 3829, 3963, 4007, 4173, 4977, 5051, 5059, 5503, 5507, 6363, 7217, 7491, 7541, 8447, 10247

Offset

1,1

Comments

Digital complement of a digit d is 10-d if d > 0, 0 otherwise.

Links

Table of n, a(n) for n=1..52.

Example

3829 is a term since 7829, 3229, 3889 and 3821 are all primes.

Mathematica

q[n_] := Module[{d = IntegerDigits[n]}, And @@ PrimeQ[Table[FromDigits[ReplacePart [d, i -> If[d[[i]] == 0, d[[i]], 10 - d[[i]]]]], {i, 1, Length[d]}]]]; Select[Range[10^4], q] (* Amiram Eldar, Jun 15 2021 *)

Prog

(Python)
from sympy import isprime
def comp(d, i): return d[:i] + str((10-int(d[i]))%10) + d[i+1:]
def ok(n):
    d = str(n)
    return all(isprime(int(comp(d, i))) for i in range(len(d)))
print(list(filter(ok, range(1, 11000)))) # Michael S. Branicky, Jun 14 2021
(PARI) f(x) = if (x, 10-x);
isok(m) = {my(d=digits(m)); for (i=1, #d, d[i] = f(d[i]); if (!isprime(fromdigits(d)), return (0)); d[i] = f(d[i]); ); return (1); } \\ Michel Marcus, Jun 15 2021

Crossrefs

Cf. A055120, A089740, A318785.

Sequence in context: A229860 A081453 A352105 * A200655 A249439 A276693

Adjacent sequences: A345340 A345341 A345342 * A345344 A345345 A345346

Keyword

nonn,base,easy,less

Author

Lamine Ngom, Jun 14 2021

Status

approved