OFFSET
1,1
COMMENTS
Any other terms have more than 20 digits. - Michael S. Branicky, Dec 19 2020
LINKS
Patrick De Geest, World!Of Palindromic Primes
EXAMPLE
373_10 = 565_8. - Jon E. Schoenfield, Apr 10 2021
MATHEMATICA
Do[s = RealDigits[n, 8][[1]]; t = RealDigits[n, 10][[1]]; If[PrimeQ[n], If[FromDigits[t] == FromDigits[Reverse[t]], If[FromDigits[s] == FromDigits[Reverse[s]], Print[n]]]], {n, 1, 10^5}]
pal810Q[p_]:=PalindromeQ[p]&&IntegerDigits[p, 8]==Reverse[IntegerDigits[p, 8]]; Select[ Prime[ Range[150000]], pal810Q] (* Harvey P. Dale, May 25 2023 *)
PROG
(Python) # efficiently search to large numbers
from sympy import isprime
from itertools import product
def candidate_prime_pals(digits):
ruled_out = "024568" # can't be even or multiple of 5
midrange = [[""], "0123456789"]
for p in product("0123456789", repeat=digits//2):
left = "".join(p)
if len(left):
if left[0] in ruled_out: continue
for middle in midrange[digits%2]:
yield left+middle+left[::-1]
for digits in range(1, 15):
for p in candidate_prime_pals(digits):
intp = int(p); octp = oct(intp)[2:]
if octp==octp[::-1]:
if isprime(intp):
print(intp, end=", ") # Michael S. Branicky, Dec 19 2020
(Python) # alternate sufficient for producing terms through a(9)
from sympy import isprime
def ispal(n): strn = str(n); return strn==strn[::-1]
for n in range(10**7):
if ispal(n) and ispal(oct(n)[2:]) and isprime(n):
print(n) # Michael S. Branicky, Dec 20 2020
(PARI) is(n) = my(d=digits(n, 8), dd=digits(n)); d==Vecrev(d) && dd==Vecrev(dd)
forprime(p=1, , if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Dec 20 2020
CROSSREFS
KEYWORD
nonn,hard,base,more
AUTHOR
Patrick De Geest, Aug 15 1998
STATUS
approved