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A253646
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Primes p such that p^k is zeroless for k=1,...,6.
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5
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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Select[Prime[Range[10^7]], Count[Flatten[IntegerDigits/@(#^Range[6])], 0] == 0&] (* Harvey P. Dale, May 26 2016 *)
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PROG
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(PARI) forprime(p=0, , forstep(k=6, 1, -1, vecmin(digits(p^k))||next(2)); print1(p", "))
(Python)
from sympy import isprime
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):
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CROSSREFS
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KEYWORD
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nonn,base,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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