A109862 Palindromic primes p such that p's 10's complement is also a prime.

3, 5, 7, 11, 191, 353, 383, 929, 10601, 11411, 12821, 13931, 14741, 15551, 16061, 16361, 16661, 17471, 30803, 32423, 33533, 36263, 72227, 74747, 75557, 76367, 76667, 93239, 94349, 94649, 94949, 97379, 1028201, 1074701, 1082801, 1300031, 1328231, 1456541, 1508051

Offset

1,1

Comments

Conjecture: Sequence is infinite.

Links

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

Example

353 is a term as 1000 - 353 = 647 is also prime.

Mathematica

Do[p = Prime[n]; If[FromDigits[Reverse[IntegerDigits[p]]] == p && PrimeQ[10^Length[IntegerDigits[p]] - p], Print[p]], {n, 1, 10^6}] (* Ryan Propper, Sep 01 2005 *)

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 [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. A109863.

Sequence in context: A159471 A068113 A068831 * A069804 A245722 A262962

Adjacent sequences: A109859 A109860 A109861 * A109863 A109864 A109865

Keyword

base,nonn

Author

Amarnath Murthy, Jul 08 2005

Extensions

More terms from Ryan Propper, Sep 01 2005

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

Status

approved