A038616 Primes not containing digit '8'.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 293, 307

Offset

1,1

Comments

Subsequence of primes of A052421. - 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, 8] == 0 &] (* Harvey P. Dale, Jan 24 2011 *)

Prog

(Magma) [ p: p in PrimesUpTo(400) | not 8 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
(PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), 8), print1(p, ", ")); ); \\ Michel Marcus, Feb 22 2015
(PARI) next_A038616(n)=until((n=nextprime(n+1))==(n=next_A052421(n-1)), ); n \\ M. F. Hasler, Jan 14 2020

Crossrefs

Intersection of A000040 (primes) and A052421 (numbers with no 8).

Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, A038615, this sequence, and A038617, respectively.

Sequence in context: A079152 A124590 A049573 * A228296 A176165 A196230

Adjacent sequences: A038613 A038614 A038615 * A038617 A038618 A038619

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