A245576 Primes p such that p and p^2 lack the zero digit in their decimal expansions.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 59, 61, 67, 73, 79, 83, 89, 113, 127, 131, 137, 139, 157, 163, 167, 173, 181, 191, 193, 211, 223, 227, 229, 233, 239, 263, 269, 271, 277, 281, 293, 311, 313, 337, 359, 367, 373, 379, 383, 389, 419, 421, 431, 433

Offset: 1

Author

Zak Seidov, Dec 25 2014

Keywords

• base
• nonn

Comments

Subsequence of A052042. First terms that are in A052042 but not here: 107, 109, 307, 409.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..3001

Crossrefs

Cf. A052042, A052043.

Programs

Mathematica

fQ[n_] := Min[IntegerDigits[n]] > 0; Select[Prime @ Range @ 90, fQ[#] && fQ[#^2] &]
Select[Prime[Range[100]],FreeQ[{IntegerDigits[#],IntegerDigits[#^2]},0]&] (* Harvey P. Dale, Jun 14 2024 *)

PARI

(vmd (n) = vecmin (digits (n))); p = 2;for (k = 1, 300, if (vmd (p) > 0 && vmd (p^2) > 0, print1 (p ", " )); p = nextprime (1 + p))

Python

from sympy import prime
A245576_list = [p for p in (prime(i) for i in range(1,10**4)) if not(str(p).count('0') or str(p**2).count('0'))]
# Chai Wah Wu, Dec 27 2014