A068876 Smallest n-digit prime with property that digits alternate in parity.

2, 23, 101, 2129, 10103, 210101, 1010129, 21010127, 101010167, 2101010147, 10101010163, 210101010187, 1010101010341, 21010101010147, 101010101010323, 2101010101010141, 10101010101010141, 210101010101010323, 1010101010101010143

Offset: 1

Author

Amarnath Murthy, Mar 19 2002

Keywords

• nonn
• base

Examples

			a(4) = 2129 as 2, 1, 2 and 9 have even and odd parity alternately.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..700

Crossrefs

Cf. A030144, A068877, A056830.

Programs

Maple

alp:= proc(n) local L,d;
L:= convert(n,base,10);
d:= nops(L);
if d::even then L:= L + map(op, [[0,1]$(d/2)]) else L:= L + map(op, [[0,1]$((d-1)/2),[0]]) fi;
nops(convert(L mod 2, set))=1
end proc:
f:= proc(d) local s;
  if d::even then s:= 2*10^(d-1)+(10^d-1)/99-1
  else s:= (10^(d+1)-1)/99-1
  fi;
  do s:= nextprime(s);
     if alp(s) then return s fi
  od
end proc:
seq(f(d),d=1..20); # Robert Israel, Aug 14 2018

Mathematica

fQ[n_] := Block[{m = Mod[ IntegerDigits@ n, 2]}, m == Split[m, UnsameQ][[1]]]; f[n_] := Block[{c = 1 + 100 (100^Ceiling[n/2 - 1] - 1)/99, k}, k = If[ OddQ@ n, c, 2*10^(n - 1) + c]; k = NextPrime[k - 1]; While[ !fQ@ k, k = NextPrime@ k]; k]; Array[f, 21] (* Robert G. Wilson v, Apr 01 2011 *)

Sage

concat = lambda x: Integer(''.join(map(str,x)),base=10)
def A068876(n):
    dd = {0:range(0,10,2), 1: range(1,10,2)}
    for d0 in [1..9]:
        if n % 2 == 0 and d0 % 2 == 1: continue # optimization
        ds = [dd[(d0+1+i) % 2] for i in range(n-1)]
        for dr in cartesian_product(ds):
            c = concat([d0]+dr)
            if is_prime(c): return c  # D. S. McNeil, Apr 02 2011

Extensions

a(9)-a(13) corrected and a(14)-a(19) from Donovan Johnson, Apr 01 2011