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A038617
Primes not containing the digit '9'.
14
2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 83, 101, 103, 107, 113, 127, 131, 137, 151, 157, 163, 167, 173, 181, 211, 223, 227, 233, 241, 251, 257, 263, 271, 277, 281, 283, 307, 311, 313, 317, 331, 337, 347, 353, 367, 373, 383, 401, 421
OFFSET
1,1
COMMENTS
Subsequence of primes of A007095. - Michel Marcus, Feb 22 2015
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
LINKS
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).
FORMULA
a(n) ~ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023
MATHEMATICA
Select[Prime[Range[1000]], DigitCount[ # ][[9]] == 0 &] (* Stefan Steinerberger, May 20 2006 *)
PROG
(Magma) [ p: p in PrimesUpTo(500) | not 9 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
(PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), 9), print1(p, ", ")); ); \\ Michel Marcus, Feb 22 2015
(PARI) lista(nn) = forprime (p=2, nn, if (vecmax(digits(p)) != 9, print1(p, ", "))); \\ Michel Marcus, Apr 06 2016
(PARI) next_A038617(n)=until((n=nextprime(n+1))==(n=next_A007095(n-1)), ); n \\ M. F. Hasler, Jan 14 2020
(Python)
from sympy import isprime
i = 1
while i <= 300:
if "9" not in str(i) and isprime(i):
print(str(i), end=", ")
i += 1 # Indranil Ghosh, Feb 07 2017
CROSSREFS
Intersection of A000040 (primes) and A007095 (numbers with no digit 9).
Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and this sequence, respectively.
Primes with other restrictions on digits: A106116, A156756.
Sequence in context: A051647 A042986 A143390 * A036962 A350535 A160337
KEYWORD
nonn,easy,base
AUTHOR
Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998
STATUS
approved