A068877 Largest n-digit prime with property that digits alternate in parity.

7, 89, 983, 8969, 98981, 898987, 9898921, 89898983, 989898989, 8989898969, 98989898981, 898989898987, 9898989898901, 89898989898967, 989898989898943, 8989898989898969, 98989898989898981, 898989898989898943, 9898989898989898789

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..500

Example

a(4) = 8969 as 8, 9, 6 and 9 have even and odd parity alternately.

Maple

alp:= proc(n) local L;
  L:= convert(n, base, 10);
  andmap(i -> (L[i] - i) mod 2 = 0, [$1..nops(L)])
end proc:
f:= proc(d) local p;
  if d::even then p:= 8*(10^d-1)/9 + (10^d-1)/99 + 1
  else p:= 8*(10^d-1)/9+(10^(d+1)-1)/99 + 1
  fi;
  do
    p:= prevprime(p);
    if alp(p) then return p fi
  od
end proc:
map(f, [$1..30]); # Robert Israel, Mar 19 2026

Prog

(SageMath)
concat = lambda x: Integer(''.join(map(str, x)), base=10)
def A068877(n):
    dd = {0:range(0, 10, 2)[::-1], 1: range(1, 10, 2)[::-1]}
    for d0 in [1..9][::-1]:
        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, A062232, A068876.

Sequence in context: A068692 A178006 A053302 * A121044 A107109 A089771

Adjacent sequences: A068874 A068875 A068876 * A068878 A068879 A068880

Keyword

nonn,base

Author

Amarnath Murthy, Mar 19 2002

Extensions

a(15)-a(19) from Donovan Johnson, Apr 01 2011

Status

approved