A038613 Primes not containing the digit '5'.

2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 263, 269, 271, 277, 281, 283, 293, 307, 311

Offset: 1

Author

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

Keywords

• nonn
• easy
• base

Comments

Subsequence of primes of A052413. - 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

Examples

			From _M. F. Hasler_, Jan 14 2020: (Start)
After a(85) = 499, the next prime without digit 5 is a(86) = 601.
After a(3734) = 49999, the next term is a(3735) = 60013.
After a(27273) = 499979, the next term is 600011.
After a(206276) = 4999999, the next term is 6000011. (End)
		

Links

• Jason Bard, Table of n, a(n) for n = 1..10000
• 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).
• Index to entries for primes with digits in a given set

Crossrefs

Intersection of A000040 (primes) and A052413 (numbers with no digit 5).

Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, this sequence, A038614, A038615, A038616, and A038617, respectively.

Programs

Magma

[ p: p in PrimesUpTo(400) | not 5 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011

Mathematica

Select[Prime[Range[70]], DigitCount[#, 10, 5] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)

PARI

lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 5), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015

PARI

(A038613_upto(n)=select( is_A052413, primes([1, n])))(350) \\ see A052413
next_A038613(n)={until(isprime(n), n=next_A052413(nextprime(n+1)-1)); n}
( {A038613_vec(n, M=1)=M--;vector(n, i, M=next_A038613(M))} )(20, 1000) \\ Compute n terms >= M. See also the OEIS wiki page. - M. F. Hasler, Jan 14 2020

Formula

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011