A038612 Primes not containing the digit '4'.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 283, 293

Offset

1,1

Comments

Subsequence of primes of A052406. - 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

Table of n, a(n) for n=1..57.

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, 4] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)

Prog

(Magma) [ p: p in PrimesUpTo(300) | not 4 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
(PARI)
lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), 4), print1(p, ", ")); ); \\ Michel Marcus, Feb 22 2015
( {A038612_upto(N)=select( is_A052406, primes([1, N]))} )(444) \\ or better:
next_A038612(n)={until(isprime(n), n=next_A052406(nextprime(n+1)-1)); n}
( {A038612_vec(n, M=1)=M--; vector(n, i, n=next_A038612(if(i>1, n)))} )(20, 1000)
\\ (See the OEIS wiki page for more.) - M. F. Hasler, Jan 12 2020

Crossrefs

Intersection of A000040 (primes) and A052406 (numbers without digit 4).

Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, this sequence, A038613, A038614, A038615, A038616, and A038617, respectively.

Sequence in context: A197298 A211654 A363998 * A012883 A296915 A171032

Adjacent sequences: A038609 A038610 A038611 * A038613 A038614 A038615

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