

A253646


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


5




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



