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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A030144, A068877, A056830.

Sequence in context: A357739 A131176 A141405 * A073175 A352164 A141888

Adjacent sequences: A068873 A068874 A068875 * A068877 A068878 A068879

Keyword

nonn,base

Author

Amarnath Murthy, Mar 19 2002

Extensions

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

Status

approved