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A046477 Primes that are palindromic in bases 8 and 10.

%I A046477 #37 May 25 2023 13:25:36
%S A046477 2,3,5,7,373,13331,30103,1496941,1970791
%N A046477 Primes that are palindromic in bases 8 and 10.
%C A046477 Any other terms have more than 20 digits. - _Michael S. Branicky_, Dec 19 2020
%H A046477 Patrick De Geest, <a href="http://www.worldofnumbers.com/palpri.htm">World!Of Palindromic Primes</a>
%e A046477 373_10 = 565_8. - _Jon E. Schoenfield_, Apr 10 2021
%t A046477 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}]
%t A046477 pal810Q[p_]:=PalindromeQ[p]&&IntegerDigits[p,8]==Reverse[IntegerDigits[p,8]]; Select[ Prime[ Range[150000]],pal810Q] (* _Harvey P. Dale_, May 25 2023 *)
%o A046477 (Python) # efficiently search to large numbers
%o A046477 from sympy import isprime
%o A046477 from itertools import product
%o A046477 def candidate_prime_pals(digits):
%o A046477   ruled_out = "024568" # can't be even or multiple of 5
%o A046477   midrange = [[""], "0123456789"]
%o A046477   for p in product("0123456789", repeat=digits//2):
%o A046477     left = "".join(p)
%o A046477     if len(left):
%o A046477       if left[0] in ruled_out: continue
%o A046477     for middle in midrange[digits%2]:
%o A046477       yield left+middle+left[::-1]
%o A046477 for digits in range(1, 15):
%o A046477   for p in candidate_prime_pals(digits):
%o A046477     intp = int(p); octp = oct(intp)[2:]
%o A046477     if octp==octp[::-1]:
%o A046477       if isprime(intp):
%o A046477         print(intp, end=", ") # _Michael S. Branicky_, Dec 19 2020
%o A046477 (Python) # alternate sufficient for producing terms through a(9)
%o A046477 from sympy import isprime
%o A046477 def ispal(n): strn = str(n); return strn==strn[::-1]
%o A046477 for n in range(10**7):
%o A046477   if ispal(n) and ispal(oct(n)[2:]) and isprime(n):
%o A046477     print(n) # _Michael S. Branicky_, Dec 20 2020
%o A046477 (PARI) is(n) = my(d=digits(n, 8), dd=digits(n)); d==Vecrev(d) && dd==Vecrev(dd)
%o A046477 forprime(p=1, , if(is(p), print1(p, ", "))) \\ _Felix Fröhlich_, Dec 20 2020
%Y A046477 Cf. A002113, A002385, A029976, A029804.
%K A046477 nonn,hard,base,more
%O A046477 1,1
%A A046477 _Patrick De Geest_, Aug 15 1998