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A038618 Primes not containing digit '0', a.k.a. zeroless primes. 31
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A052382 and A000040; A168046(a(n))*A010051(a(n))=1. - Reinhard Zumkeller, Dec 01 2009

Complement of A056709 with respect to primes (A000040). - Lekraj Beedassy, Jul 04 2010

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

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

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

Eric Weisstein's World of Mathematics, Zerofree

MATHEMATICA

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

PROG

(MAGMA) [ p: p in PrimesUpTo(300) | not 0 in Intseq(p) ];  // Bruno Berselli, Aug 08 2011

(PARI) is(n)=if(isprime(n), n=vecsort(eval(Vec(Str(n))), , 8); n[1]>0) \\ Charles R Greathouse IV, Aug 09 2011

(PARI) lista(nn) = forprime (p=2, nn, if (vecmin(digits(p)), print1(p, ", "))); \\ Michel Marcus, Apr 06 2016

(Haskell)

a038618 n = a038618_list !! (n-1)

a038618_list = filter ((== 1) . a168046) a000040_list

-- Reinhard Zumkeller, Apr 07 2014, Sep 27 2011

CROSSREFS

Cf. A000040, A010051, A052382, A168046.

Subsequence of A195943.

Sequence in context: A052085 A082646 A231588 * A030475 A069676 A062353

Adjacent sequences:  A038615 A038616 A038617 * A038619 A038620 A038621

KEYWORD

nonn,easy,base

AUTHOR

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

STATUS

approved

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Last modified October 18 20:24 EDT 2019. Contains 328197 sequences. (Running on oeis4.)