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A164968 Naughty primes: primes in which the number of zeros is greater than the number of all other digits. 8
10007, 10009, 40009, 70001, 70003, 70009, 90001, 90007, 100003, 200003, 200009, 300007, 400009, 500009, 700001, 900001, 900007, 1000003, 1000033, 1000037, 1000039, 1000081, 1000099, 1000303, 1000403, 1000409, 1000507, 1000609, 1000907, 1001003, 1003001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(31) = 1003001 is the smallest palindromic naughty prime. - M. F. Hasler, Nov 22 2009

This sequence can be considered as irregular table in which row n lists the terms with n digits. The row lengths (number of terms with n digits) are then 0, 0, 0, 0, 8, 9, 296, 275, 7934, 9527, 235729, ... - M. F. Hasler, Jul 13 2018

LINKS

M. F. Hasler and Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000 (first 5000 terms from M. F. Hasler).

Chris Caldwell, The Prime Glossary, Naughty prime.

EXAMPLE

a(24) = 1000303 is a naughty prime because the number of zeros is greater than the number of all other digits.

MAPLE

Q[1]:= [seq([i], i=1..9)]:

for d from 2 to 6 do Q[d]:= map(t -> seq([i, op(t)], i=1..9), Q[d-1]) od:

F:= proc(d) local R, dn, s, sp, q, x;

   R:= NULL;

   for dn from 2 to floor((d-1)/2) do

      for s in combinat:-choose([$1..d-2], dn-2) do

        sp:= [0, op(s), d-1];

        for q in Q[dn] do

          x:= add(q[i]*10^sp[i], i=1..dn);

          if isprime(x) then R:= R, x fi;

    od od od;

    sort([R])

end proc:

seq(op(F(d)), d=5..7); # Robert Israel, Jul 10 2018

MATHEMATICA

lst = {}; Do[If[PrimeQ[n] && Count[IntegerDigits[n], 0] > IntegerLength[n]/2, AppendTo[lst, n]], {n, 10^4 + 1, 3^13, 2}]; lst (* Arkadiusz Wesolowski, Sep 18 2011 *)

Select[Prime[Range[100000]], DigitCount[#, 10, 0]>IntegerLength[#]/2&] (* Harvey P. Dale, Jun 09 2015 *)

PROG

(PARI) next_A164968(p)={ for( n=#Str(p)\2+1, oo, my(L=10^(2*n+1)); p=max(10^(2*n-3), p); while( L>p=nextprime(p+1), vecsort(Vecsmall(Str(p)))[n]>48 || return(p)); p=0) } \\ M. F. Hasler, Nov 22 2009, syntax update Jul 10 2018

(PARI) A164968_row(n, a=List(), t=vectorv(n, i, 10^(n-i)))={for(z=2, (n-1)\2, my(v=vector(z, i, if(i<2, [1, 1], i<z, [2, n-1], [n, n]))); forvec(d=vector(z, i, [1, 9]), bittest(650, d[z])&& vecsum(d)%3&& forvec(p=v, isprime(d*vecextract(t, p))&& listput(a, d*vecextract(t, p)), 2))); Set(a)} \\ M. F. Hasler, Jul 13 2018

CROSSREFS

Sequence in context: A082567 A031598 A210760 * A165296 A182697 A101442

Adjacent sequences:  A164965 A164966 A164967 * A164969 A164970 A164971

KEYWORD

base,nonn

AUTHOR

G. L. Honaker, Jr., Sep 02 2009

STATUS

approved

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Last modified October 20 17:28 EDT 2019. Contains 328268 sequences. (Running on oeis4.)