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A038618
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Primes not containing the decimal digit 0, a.k.a. zeroless or zerofree primes.
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43
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Complement of A056709 with respect to primes (A000040). - Lekraj Beedassy, Jul 04 2010
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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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Eric Weisstein's World of Mathematics, Zerofree
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FORMULA
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Intersection of A052382 (zeroless numbers) and A000040 (primes); A168046(a(n))*A010051(a(n)) = 1. - Reinhard Zumkeller, Dec 01 2009
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MATHEMATICA
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Select[Prime[Range[70]], DigitCount[#, 10, 0] == 0 &] (* Vincenzo Librandi, Aug 09 2011 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(300) | not 0 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
(PARI) is(n)=if(isprime(n), n=vecsort(eval(Vec(Str(n))), , 8); n[1]>0) \\ Charles R Greathouse IV, Aug 09 2011
(PARI) lista(nn) = forprime (p=2, nn, if (vecmin(digits(p)), print1(p, ", "))); \\ Michel Marcus, Apr 06 2016
(PARI) {next_A038618(n)=until(vecmin(digits(n=nextprime(next_A052382(n)))), ); n} \\ Cf. OEIS Wiki page (LINKS) for other programs. - M. F. Hasler, Jan 12 2020
(Haskell)
a038618 n = a038618_list !! (n-1)
a038618_list = filter ((== 1) . a168046) a000040_list
-- Reinhard Zumkeller, Apr 07 2014, Sep 27 2011
(Python)
from sympy import primerange
def aupto(N): return [p for p in primerange(1, N+1) if '0' not in str(p)]
print(aupto(300)) # Michael S. Branicky, Mar 11 2022
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CROSSREFS
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Cf. A010051, A168046.
Subsequence of A000040 (primes), A052382 (zeroless numbers) and A195943.
Primes having no digit d = 0..9 are this sequence, A038603, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.
Sequence in context: A052085 A082646 A231588 * A030475 A069676 A062353
Adjacent sequences: A038615 A038616 A038617 * A038619 A038620 A038621
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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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STATUS
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approved
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