A386528 Primes which remain primes after the mapping {1 -> 3, 3 -> 5, 5 -> 7, 7 -> 9, 9 -> 1} of its decimal digits.

2, 3, 5, 19, 31, 37, 41, 59, 97, 131, 137, 151, 157, 181, 191, 199, 211, 227, 239, 271, 281, 307, 349, 359, 367, 409, 419, 457, 461, 479, 509, 541, 569, 619, 631, 641, 691, 727, 797, 821, 827, 829, 881, 907, 919, 947, 971, 977, 991, 1009, 1021, 1049, 1069, 1087, 1097, 1109, 1151

Offset: 1

Author

Tristan J. Jones and Robert G. Wilson v, Aug 21 2025

Keywords

• base
• nonn
• new

Comments

Of the 10! possible nontrivial decimal digital mappings, this one was chosen for its inclusion of all the odd numbers and none of the even numbers.

Examples

			19 is a term since the mapping produces 31, which is prime;
31 is a term since the mapping produces 53, which is prime.
		

Crossrefs

Cf. A000040, A198047.

Programs

Mathematica

fQ[n_] := PrimeQ[ FromDigits[ IntegerDigits[ n] /. {1 -> 3, 3 -> 5, 5 -> 7, 7 -> 9, 9 -> 1}]]; Select[ Prime@ Range@ 200, fQ]

Python

from sympy import isprime
def ok(n): return isprime(n) and isprime(int(str(n).translate(str.maketrans("13579","35791"))))
print([k for k in range(1200) if ok(k)]) # Michael S. Branicky, Aug 24 2025