A352382 Numbers k such that no nonzero digit of 5*k divides 5*k.

74, 76, 86, 94, 98, 134, 146, 152, 156, 158, 166, 172, 174, 178, 194, 196, 614, 674, 676, 686, 694, 698, 734, 740, 746, 752, 754, 758, 766, 772, 778, 794, 796, 806, 814, 818, 866, 874, 878, 886, 894, 898, 926, 934, 938, 946, 954, 958, 974, 978, 986, 998, 1214, 1276, 1286, 1294, 1298, 1334, 1340

Offset: 1

Author

Eric Angelini and Carole Dubois, Mar 14 2022

Keywords

• base
• nonn

Comments

Only even terms (see the last line of the Example section to understand why).

Examples

			a(1) = 74 and 5*74 = 370 is not divisible by 3, 7 or 0;
a(2) = 76 and 5*76 = 380 is not divisible by 3, 8 or 0;
a(3) = 86 and 5*86 = 430 is not divisible by 4, 3 or 0;
a(4) = 94 and 5*94 = 470 is not divisible by 4, 7 or 0; etc.
93 is not in the sequence as 5*93 = 465 is divisible by 5.
		

Crossrefs

Cf. A038772, A352379, A352380, A352381.

Programs

Mathematica

q[n_] := AllTrue[IntegerDigits[5*n], # == 0 || !Divisible[5*n, #] &]; Select[Range[1340], q] (* Amiram Eldar, Mar 14 2022 *)

Python

def ok(n): return not any(5*n%int(d)==0 for d in set(str(5*n)) if d!='0')
print([k for k in range(1, 1277) if ok(k)]) # Michael S. Branicky, Mar 14 2022