A038611 Primes not containing the digit '3'.

2, 5, 7, 11, 17, 19, 29, 41, 47, 59, 61, 67, 71, 79, 89, 97, 101, 107, 109, 127, 149, 151, 157, 167, 179, 181, 191, 197, 199, 211, 227, 229, 241, 251, 257, 269, 271, 277, 281, 401, 409, 419, 421, 449, 457, 461, 467, 479, 487, 491, 499, 509, 521, 541, 547, 557

Offset

1,1

Comments

Subsequence of primes of A052405. - 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[70]], DigitCount[#, 10, 3] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)

Prog

(Magma) [ p: p in PrimesUpTo(600) | not 3 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
(PARI)
lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), 3), print1(p, ", ")); ); \\ Michel Marcus, Feb 22 2015
(PARI)
( {A038611_upto(N, M=1)=select( is_A052405, primes([M, N]))} )(350)
(PARI)
next_A038611(n)={until((n=nextprime(n+1))==n=next_A052405(n-1), ); n}
( {A038611_vec(n, M=2)=M--; vector(n, i, M=next_A038611(M))} )(20, 1000)
\\ Get 20 terms >= 1000. See also OEIS wiki page. - M. F. Hasler, Jan 14 2020
(Python)
from sympy import isprime
i=j=1
while j<=5000:
    if isprime(i) and "3" not in str(i):
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 07 2017

Crossrefs

Intersection of A000040 (primes) and A052405 (numbers with no digit 3).

Primes having no digit d = 0..9 are A038618, A038603, A038604, this sequence, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.

Sequence in context: A323698 A045348 A023207 * A265761 A023213 A162575

Adjacent sequences: A038608 A038609 A038610 * A038612 A038613 A038614

Keyword

nonn,easy,base

Author

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

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

Status

approved