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A038614
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Primes not containing the digit '6'.
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12
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 271, 277, 281, 283, 293, 307, 311
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internal format)
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OFFSET
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1,1
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COMMENTS
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Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016
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LINKS
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FORMULA
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MAPLE
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no6:= proc(n) option remember;
n mod 10 <> 6 and procname(floor(n/10))
end proc:
no6(0):= true:
select(no6 and isprime, [2, seq(i, i=3..1000, 2)]); # Robert Israel, Mar 16 2017
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MATHEMATICA
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Select[Prime[Range[70]], DigitCount[#, 10, 6] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(400) | not 6 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
(PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), 6), print1(p, ", ")); ); \\ Michel Marcus, Feb 22 2015
(PARI)
(A038614_upto(n)=select( is_A038614, primes([1, n])))(350) \\ needs the above
next_A038614(n)={until(isprime(n), n=next_A052414(nextprime(n+1)-1)); n}
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CROSSREFS
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Intersection of A000040 (primes) and A052414 (numbers with no digit 6).
Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, this sequence, A038615, A038616, and A038617, respectively.
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KEYWORD
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nonn,easy,base
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AUTHOR
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Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998
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EXTENSIONS
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STATUS
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approved
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