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A091637 Number of primes less than 10^n which do not contain the digit 3. 10
3, 16, 102, 668, 4715, 34813, 265015, 2067152, 16413535, 132200223, 1076692515, 8849480283, 73288053795, 610860050965 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..14.

FORMULA

Number of primes less than 10^n after removing any primes with at least one digit 3.

a(n) = A006880(n) - A091647(n).

EXAMPLE

a(2)=16 because there are 25 primes less than 10^2, 9 have at least one digit 3; 25-9 = 16.

MATHEMATICA

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 3] == {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)

Table[Count[Prime[Range[PrimePi[10^n]]], _?(DigitCount[#, 10, 3]==0&)], {n, 8}] (* Harvey P. Dale, Oct 04 2011 *)

PROG

(PARI) good(n)=n=eval(Vec(Str(n))); for(i=1, #n, if(n[i]==3, return(1))); 0

a(n)=my(s); forprime(p=2, 10^n, s+=good(p)); s \\ Charles R Greathouse IV, Oct 04 2011

CROSSREFS

Cf. A091634, A091635, A091636, A091638, A091639, A091640, A091641, A091642, A091643.

Sequence in context: A009151 A009007 A000949 * A278429 A207434 A074542

Adjacent sequences:  A091634 A091635 A091636 * A091638 A091639 A091640

KEYWORD

nonn,base

AUTHOR

Enoch Haga, Jan 30 2004

EXTENSIONS

Edited and extended by Robert G. Wilson v, Feb 02 2004

a(9)-a(12) from Donovan Johnson, Feb 14 2008

a(13) from Robert Price, Nov 08 2013

a(14) from Giovanni Resta, Mar 20 2017

STATUS

approved

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Last modified October 14 09:25 EDT 2019. Contains 327995 sequences. (Running on oeis4.)