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A045336 Palindromic terms from A019546.

%I A045336 #35 Mar 24 2025 16:01:50
%S A045336 2,3,5,7,353,373,727,757,32323,33533,35353,35753,37273,37573,72227,
%T A045336 72727,73237,75557,77377,3222223,3223223,3233323,3252523,3272723,
%U A045336 3337333,3353533,3553553,3722273,3732373,3773773,7257527,7327237,7352537,7527257,7722277
%N A045336 Palindromic terms from A019546.
%C A045336 a(33) = 7352537 is the smallest palindromic prime using all prime digits (see Prime Curios! link). - _Bernard Schott_, Nov 10 2020
%H A045336 Michael S. Branicky, <a href="/A045336/b045336.txt">Table of n, a(n) for n = 1..12725</a> (all terms with <= 17 digits; terms 1..330 from Harvey P. Dale)
%H A045336 Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?short=7352537">7352537</a>, Prime Curios!
%t A045336 Select[ Range[ 1, 10^7 ], PrimeQ[ # ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 0 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 1 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 4 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 6 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 8 ] && FreeQ[ RealDigits[ # ][ [ 1 ] ], 9 ] && RealDigits[ # ][ [ 1 ] ] == Reverse[ RealDigits[ # ][ [ 1 ] ] ] & ]
%t A045336 Table[FromDigits/@Select[Tuples[{2,3,5,7},n],#==Reverse[#]&&PrimeQ[ FromDigits[ #]]&],{n,12}]//Flatten (* _Harvey P. Dale_, Jun 19 2016 *)
%t A045336 Select[Flatten[Table[FromDigits/@Tuples[{2,3,5,7},n],{n,10}]],PrimeQ[#]&&PalindromeQ[#]&] (* _Harvey P. Dale_, Mar 24 2025 *)
%t A045336 f@n_ := Prime@n;
%t A045336 g@l_ := FromDigits@# & /@ Table[Join[l, {f@i}, Reverse@l], {i, 4}];
%t A045336 Flatten[g@# & /@ (f@# & /@
%t A045336      Select[Table[IntegerDigits[n, 5], {n, 2000}], FreeQ[#, 0] &])] //
%t A045336 Select[PrimeQ] (* _Hans Rudolf Widmer_, Dec 18 2021 *)
%o A045336 (Python)
%o A045336 from sympy import isprime
%o A045336 from itertools import count, product, takewhile
%o A045336 def primedigpals():
%o A045336     for d in count(1, 2):
%o A045336         for p in product("2357", repeat=d//2):
%o A045336             left = "".join(p)
%o A045336             for mid in "2357":
%o A045336                 yield int(left + mid + left[::-1])
%o A045336 def aupto(N):
%o A045336     return list(takewhile(lambda x: x<=N, filter(isprime, primedigpals())))
%o A045336 print(aupto(10**7)) # _Michael S. Branicky_, Dec 18 2021
%Y A045336 Cf. A019546 and A002385.
%K A045336 nonn,base
%O A045336 1,1
%A A045336 _Robert G. Wilson v_, Aug 18 2000