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

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A052042, A052043.

Sequence in context: A049555 A281295 A052042 * A086472 A219669 A109611

Adjacent sequences: A245573 A245574 A245575 * A245577 A245578 A245579

Keyword

base,nonn

Author

Zak Seidov, Dec 25 2014

Status

approved