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A038603 Primes not containing digit '1'. 14
2, 3, 5, 7, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 83, 89, 97, 223, 227, 229, 233, 239, 257, 263, 269, 277, 283, 293, 307, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 409, 433, 439, 443, 449, 457, 463, 467, 479, 487, 499, 503, 509, 523, 547, 557 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A132080. - Reinhard Zumkeller, Aug 09 2007

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 (terms 1..1000 from R. Zumkeller)

James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.

MATHEMATICA

Select[Prime[Range[70]], DigitCount[#, 10, 1] == 0 &] (* Vincenzo Librandi, Aug 09 2011 *)

PROG

(MAGMA) [ p: p in PrimesUpTo(600) | not 1 in Intseq(p) ];  // Bruno Berselli, Aug 08 2011

(PARI) is(n)=if(isprime(n), n=vecsort(eval(Vec(Str(n))), , 8); n[1]>1||(!n[1]&&n[2]>1)) \\ Charles R Greathouse IV, Aug 09 2011

(PARI) is(n)=!vecsearch(vecsort(digits(n)), 1) && isprime(n) \\ Charles R Greathouse IV, Oct 03 2012

(Python)

from sympy import isprime

i=j=1

while j<=50000:

....if isprime(i)==True and str(i).count("1")==0:

........print str(j)+" "+str(i)

........j+=1

....i+=1 # Indranil Ghosh, Feb 07 2017

CROSSREFS

Cf. A000040.

Primes with restrictions on digits: A038603, A038604, A038611, A038612, A038613, A038614, A038615, A038616, A038617, A038618, A106116, A156756.

Sequence in context: A069867 A320585 A024770 * A106116 A091727 A240920

Adjacent sequences:  A038600 A038601 A038602 * A038604 A038605 A038606

KEYWORD

nonn,easy,base

AUTHOR

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

STATUS

approved

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)