A038617 Primes not containing the digit '9'.

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

Indranil Ghosh, Table of n, a(n) for n = 1..50000

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

Adjacent sequences: A038614 A038615 A038616 * A038618 A038619 A038620

Keyword

nonn,easy,base

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Status

approved