A109863 Primes arising as the 10's complement of A109862(n).

7, 5, 3, 89, 809, 647, 617, 71, 89399, 88589, 87179, 86069, 85259, 84449, 83939, 83639, 83339, 82529, 69197, 67577, 66467, 63737, 27773, 25253, 24443, 23633, 23333, 6761, 5651, 5351, 5051, 2621, 8971799, 8925299, 8917199, 8699969, 8671769, 8543459, 8491949

Offset

1,1

Comments

a(n) - 1 is a palindrome. Obviously 7, 5 and 3 are the only palindromic terms. Conjecture: Sequence is infinite.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

353 is a member of A109862 and 647 = 1000 - 353 corresponds to it.

Prog

(Python)
from sympy import isprime
from itertools import product
def tc(n): return 10**len(str(n)) - n
def cond(p): return isprime(p) and isprime(tc(p))
def palcands(digs):
    if digs == 1:   yield from [2, 3, 5, 7]; return
    if digs%2 == 0: yield from [[], [11]][digs==2]; return
    for first in "1379":
        for p in product("0123456789", repeat=(digs-2)//2):
            left = first + "".join(p)
            for mid in "0123456789": yield int(left + mid + left[::-1])
def auptod(digs):
    return [tc(p) for d in range(1, digs+1) for p in palcands(d) if cond(p)]
print(auptod(7)) # Michael S. Branicky, Jul 05 2021

Crossrefs

Cf. A109862.

Sequence in context: A090289 A160670 A145985 * A179177 A021574 A021061

Adjacent sequences: A109860 A109861 A109862 * A109864 A109865 A109866

Keyword

base,nonn

Author

Amarnath Murthy, Jul 08 2005

Extensions

More terms from Joshua Zucker, May 08 2006

Corrected by T. D. Noe, Nov 15 2006

a(37) and beyond from Michael S. Branicky, Jul 05 2021

Status

approved