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A038613 Primes not containing the digit '5'. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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).

EXAMPLE

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)

MATHEMATICA

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

PROG

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

(PARI)

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

(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

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.

Sequence in context: A088905 A045319 A178943 * A075235 A020634 A173555

Adjacent sequences:  A038610 A038611 A038612 * A038614 A038615 A038616

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

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Last modified May 12 13:46 EDT 2021. Contains 343823 sequences. (Running on oeis4.)