A352379 Numbers k such that no nonzero digit of 2*k divides 2*k.

17, 19, 23, 27, 28, 29, 34, 37, 38, 39, 43, 47, 49, 154, 167, 169, 173, 178, 179, 185, 187, 188, 190, 193, 194, 197, 199, 203, 215, 217, 223, 227, 229, 233, 235, 237, 239, 245, 247, 249, 253, 254, 268, 269, 277, 278, 279, 283, 289, 293, 294, 298, 299, 317, 319, 323, 328, 329, 334, 335, 337, 338, 343

Offset

1,1

Comments

There are no terms between and including 500 and 1500 and there are no terms between and including 5000 and 15000. - Harvey P. Dale, Apr 05 2025

Links

Harvey P. Dale, Table of n, a(n) for n = 1..5000

Example

a(1) = 17 and 2*17 = 34 is not divisible by 3 or 4;
a(2) = 19 and 2*19 = 38 is not divisible by 3 or 8;
a(3) = 23 and 2*23 = 46 is not divisible by 4 or 6;
a(4) = 27 and 2*27 = 54 is not divisible by 5 or 4; etc.
31 is not in the sequence as 2*31 = 62 is divisible by 2.

Mathematica

q[n_] := AllTrue[IntegerDigits[2*n], # == 0 || !Divisible[2*n, #] &]; Select[Range[350], q] (* Amiram Eldar, Mar 14 2022 *)
nnzdQ[n_]:=NoneTrue[Mod[2 n, Select[IntegerDigits[2 n], #!=0&]], #==0&]; Select[Range[350], nnzdQ] (* Harvey P. Dale, Apr 05 2025 *)

Prog

(Python)
def ok(n): return not any(2*n%int(d)==0 for d in set(str(2*n)) if d!='0')
print([k for k in range(1, 344) if ok(k)]) # Michael S. Branicky, Mar 14 2022

Crossrefs

Cf. A038772, A352380, A352381, A352382.

Sequence in context: A354880 A054484 A054796 * A322275 A008366 A126769

Adjacent sequences: A352376 A352377 A352378 * A352380 A352381 A352382

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Mar 14 2022

Status

approved