A253646 Primes p such that p^k is zeroless for k=1,...,6.

2, 3, 5, 17, 48989, 5453971, 61636943111479, 128359315177123, 884785266899689, 1116777231836989

Offset

1,1

Comments

Primes in A253647; both sequences are conjectured to be finite.

The motivation for this sequence lies in the fact that many small primes satisfy the restriction up to k=5 (there are 52 terms below 10^6, cf. A253645), but including k=6 makes the sequence much sparser, with only one term between 17 and 5*10^6, and only one more term below 2*10^9.

The terms 2, 3 and 5 seem to be the only primes in A124648, i.e., satisfy the restriction up to k=7.

a(7) > 10^11. - Chai Wah Wu, Jan 10 2015

a(11) > 3.3*10^16. - Giovanni Resta, Sep 06 2018

Links

Table of n, a(n) for n=1..10.

Mathematica

Select[Prime[Range[10^7]], Count[Flatten[IntegerDigits/@(#^Range[6])], 0] == 0&] (* Harvey P. Dale, May 26 2016 *)

Prog

(PARI) forprime(p=0, , forstep(k=6, 1, -1, vecmin(digits(p^k))||next(2)); print1(p", "))
(Python)
from sympy import isprime
A253646_list = [2]
for i in range(1, 10**6, 2):
....if not '0' in str(i):
........m = i
........for k in range(5):
............m *= i
............if '0' in str(m):
................break
........else:
............if isprime(i):
................A253646_list.append(i) # Chai Wah Wu, Jan 10 2015

Crossrefs

Cf. A253647, A253645, A124648.

Sequence in context: A275159 A127063 A127837 * A004249 A268210 A121510

Adjacent sequences: A253643 A253644 A253645 * A253647 A253648 A253649

Keyword

nonn,base,hard,more

Author

Zak Seidov and M. F. Hasler, Jan 07 2015

Extensions

a(7)-a(10) from Giovanni Resta, Sep 03 2018

Status

approved