A038614 - OEIS

A038614

Primes not containing the digit '6'.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 271, 277, 281, 283, 293, 307, 311

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OFFSET

1,1

COMMENTS

Subsequence of primes of A052414. - 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

Robert Israel, 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).

FORMULA

Intersection of A000040 and A052414. - M. F. Hasler, Jan 12 2020

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

MAPLE

no6:= proc(n) option remember;

n mod 10 <> 6 and procname(floor(n/10))

end proc:

no6(0):= true:

select(no6 and isprime, [2, seq(i, i=3..1000, 2)]); # Robert Israel, Mar 16 2017

MATHEMATICA

Select[Prime[Range[70]], DigitCount[#, 10, 6] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)

PROG

(Magma) [ p: p in PrimesUpTo(400) | not 6 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011

(PARI) lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p), , 8), 6), print1(p, ", ")); ); \\ Michel Marcus, Feb 22 2015

(PARI)

select( {is_A038614(n)=is_A052414(n)&&isprime(n)}, [1..350]) \\ see A052414

(A038614_upto(n)=select( is_A038614, primes([1, n])))(350) \\ needs the above

next_A038614(n)={until(isprime(n), n=next_A052414(nextprime(n+1)-1)); n}

(A038614_vec(n)=vector(n, i, n=next_A038614(if(i>1, n))))(66) \\ M. F. Hasler, Jan 12 2020

CROSSREFS

Intersection of A000040 (primes) and A052414 (numbers with no digit 6).

Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, this sequence, A038615, A038616, and A038617, respectively.

Sequence in context: A322443 A219697 A078668 * A171047 A050246 A229106

Adjacent sequences: A038611 A038612 A038613 * A038615 A038616 A038617

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