A046477 Primes that are palindromic in bases 8 and 10.
2, 3, 5, 7, 373, 13331, 30103, 1496941, 1970791
Offset: 1
Examples
373_10 = 565_8. - _Jon E. Schoenfield_, Apr 10 2021
Links
- Patrick De Geest, World!Of Palindromic Primes
Programs
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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 *) -
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
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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
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