A038603 Primes not containing the digit '1'.

2, 3, 5, 7, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 83, 89, 97, 223, 227, 229, 233, 239, 257, 263, 269, 277, 283, 293, 307, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 409, 433, 439, 443, 449, 457, 463, 467, 479, 487, 499, 503, 509, 523, 547, 557

Offset

1,1

Comments

Subsequence of A132080. - Reinhard Zumkeller, Aug 09 2007

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 (terms 1..1000 from R. Zumkeller)

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[70]], DigitCount[#, 10, 1] == 0 &] (* Vincenzo Librandi, Aug 09 2011 *)

Prog

(Magma) [ p: p in PrimesUpTo(600) | not 1 in Intseq(p) ];  // Bruno Berselli, Aug 08 2011
(PARI) is(n)=if(isprime(n), n=vecsort(eval(Vec(Str(n))), , 8); n[1]>1||(!n[1]&&n[2]>1)) \\ Charles R Greathouse IV, Aug 09 2011
(PARI) is(n)=!vecsearch(vecsort(digits(n)), 1) && isprime(n) \\ Charles R Greathouse IV, Oct 03 2012
(PARI) next_A038603(n)=until((n=nextprime(n+1))==n=next_A052383(n-1), ); n \\ Compute least a(k) > n. See A052383. - M. F. Hasler, Jan 14 2020
(Python)
from sympy import nextprime
i=p=1
while i<=500:
    p = nextprime(p)
    if '1' not in str(p):
        print(str(i)+" "+str(p))
        i+=1
# Indranil Ghosh, Feb 07 2017, edited by M. F. Hasler, Jan 15 2020
# See the OEIS Wiki page for more efficient programs. - M. F. Hasler, Jan 14 2020

Crossrefs

Intersection of A000040 (primes) and A052383 (numbers with no digit 1).

Primes having no digit d = 0..9 are A038618, this sequence, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.

Primes with other restrictions on digits: A106116, A156756.

Sequence in context: A069867 A320585 A024770 * A106116 A091727 A240920

Adjacent sequences: A038600 A038601 A038602 * A038604 A038605 A038606

Keyword

nonn,easy,base

Author

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

Status

approved