A046477 Primes that are palindromic in bases 8 and 10.

2, 3, 5, 7, 373, 13331, 30103, 1496941, 1970791, 34125703495359430752143

Offset

1,1

Comments

a(11) > 10^34 if it exists. - Max Alekseyev, Jun 03 2026

Links

Table of n, a(n) for n=1..10.

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

Intersection of A002385 and A029976.

Primes in A029804.

Subsequence of A002113.

Primes that are palindromic in bases 10 and b: A046472 (b=2), A046473 (b=3), A046474 (b=4), A046475 (b=6), A046476 (b=7), A046478 (b=9), A046479 (b=11), A046480 (b=12), A046481 (b=13), A046482 (b=14), A046483 (b=15), A046484 (b=16).

Sequence in context: A359491 A045336 A083183 * A360789 A145843 A090720

Adjacent sequences: A046474 A046475 A046476 * A046478 A046479 A046480

Keyword

nonn,hard,base,more,changed

Author

Patrick De Geest, Aug 15 1998

Extensions

a(10) from Max Alekseyev, Sep 14 2025

Status

approved