A253643 Numbers n such that n^k is zeroless for k=0,...,3.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 31, 35, 36, 38, 39, 41, 44, 46, 54, 56, 57, 58, 61, 62, 65, 66, 68, 72, 75, 76, 77, 81, 82, 83, 85, 88, 91, 92, 96, 111, 113, 114, 119, 121, 122, 125, 129, 132, 133, 136, 137, 139, 146, 154, 156, 157, 158, 161

Offset: 1

Author

M. F. Hasler, Mar 09 2015

Keywords

• nonn
• base
• easy

Comments

See A252484 for the subsequence of numbers having this property up to k=4.

Crossrefs

Cf. A052382, A252484 (k <= 4), A253644 (k <= 5), A253645 (primes, k <= 5), A253647 (k <= 6), A253646 (primes, k <= 6), A124648 (k <= 7), A124649 (k <= 8).

Cf. A104264.

Programs

Mathematica

Select[Range[200],AllTrue[#^Range[3],DigitCount[#,10,0]==0&]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 15 2015 *)

PARI

is_A253643(n,K=3)=!forstep(k=K,1,-1,vecmin(digits(n^k))||return)

Python

for n in range(100):
  s1,s2,s3 = str(n),str(n**2),str(n**3)
  if s1.find('0') + s2.find('0') + s3.find('0') == -3:
    print(n,end=', ') # Derek Orr, Mar 09 2015