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

Author

Amarnath Murthy, Mar 19 2002

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Cf. A030144, A068876.

Programs

Sage

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]

Extensions

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