This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A070247 #18 Sep 04 2025 18:36:44
%S A070247 5,131,10301,1003001,100030001,100111001,101000010000101,
%T A070247 10000010101000001,101000000010000000101,110000000010000000011,
%U A070247 10000000000300000000001,10000100000100000100001,100000100000010000001000001,10000000000000300000000000001,10000000001000100010000000001
%N A070247 Palindromic primes with digit sum 5.
%C A070247 It is conjectured that are just 3 palindromic primes with digit sum 2, namely 2, 11 and 101. If any others exist, they must be of the form 10^(2^k) + 1 with k > 14.
%C A070247 From _Jeppe Stig Nielsen_, Aug 30 2025: (Start)
%C A070247 It is now known that any additional primes 10^(2^k) + 1 must have k >= 31.
%C A070247 Digit sum 3 yields only one prime, 3, a palindrome in a vacuous way.
%C A070247 Digit sum 4 leads to primes (A062339), but such numbers can never be palindromes. Proof: Let w be any palindrome with digit sum 4. So w = 10^a + 10^b + 10^c + 10^d with a >= b >= c >= d >= 0. But then 10^c + 10^d is a nontrivial divisor of w, showing that w is not prime.
%C A070247 You may have come here searching for the subsequence 5, 131, 10301, 1003001, 100030001, 10000000000300000000001, ... where the largest digit exceeds 1. See A171376 and A100028 for information on them.
%C A070247 (End)
%H A070247 Jeppe Stig Nielsen, <a href="/A070247/b070247.txt">Table of n, a(n) for n = 1..386</a> (all terms below 10^1000; terms n = 1..238 from Chai Wah Wu)
%H A070247 Hans Riesel, <a href="https://doi.org/10.1090/S0025-5718-1969-0245507-6">Some factors of the numbers Gn = 6^2^n+1 and Hn = 10^2^n+1,</a> Math. Comp. 23 (1969), p. 413-415. With errata reported in Math. Comp. 24 (1970), p. 243.
%t A070247 Do[p = Join[ IntegerDigits[n, 4], Reverse[ Drop[ IntegerDigits[n, 4], -1]]]; q = Plus @@ p; If[q == 5 && PrimeQ[ FromDigits[p]] && q == 5, Print[ FromDigits[p]]], {n, 1, 4 10^8}] (* this coding will not pick up the first entry *)
%o A070247 (PARI) for(i=0,50,for(j=0,i,p=10^(2*i)+10^(i+j)+10^i+10^(i-j)+1;isprime(p)&&print1(p,", "))) \\ _Jeppe Stig Nielsen_, Aug 30 2025
%Y A070247 Cf. A002385, A062341, A070248, A070249.
%K A070247 base,nonn,changed
%O A070247 1,1
%A A070247 _Amarnath Murthy_, May 05 2002
%E A070247 Edited by _Robert G. Wilson v_, May 15 2002
%E A070247 More terms from _Chai Wah Wu_, Nov 25 2015