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 A273906 #48 Dec 08 2024 18:30:23
%S A273906 11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,113,
%T A273906 199,211,223,227,229,233,277,311,331,337,433,443,449,499,557,577,599,
%U A273906 661,677,733,773,811,877,881,883,887,911,977,991,997,1013,1019,1117,1151,1171,1181
%N A273906 Primes equal to the concatenation of two nonzero palindromic numbers.
%C A273906 The only palindrome in this sequence below 10^9 is 11 (per request of _Giovanni Teofilatto_). A004022 is a subsequence. - _David A. Corneth_, Jun 10 2016
%C A273906 If we have a concatenation of two palindromes A = A', B = B' which is palindromic, concat(A,B) =: A.B = (A.B)' = B'.A' = B.A, then A*(10^LB-1) = B*(10^LA-1) (LX = length of X) <=> A*R(LB) = B*R(LA), where R(n) = (10^n-1)/9. To have A.B prime we also must have gcd(A,B) = 1, thus A | R(LA) and B | R(LB). Such numbers are listed in A249647 (not A014950), the only palindromes there are of the form 1...1, 3...3 or 9...9. Thus the only palindromic terms in this sequence A273906 are the repunit primes A004022. - _M. F. Hasler_, Jun 10 2016
%H A273906 David A. Corneth, <a href="/A273906/b273906.txt">Table of n, a(n) for n = 1..25912</a>
%H A273906 David A. Corneth, <a href="/A273906/a273906.gp.txt">PARI program</a>
%F A273906 a(n) = A096489(n+1), n=1..21. - _R. J. Mathar_, Jun 12 2016. (This is a pure accident, I think, since A096489 is a finite sequence. - _N. J. A. Sloane_, Jun 12 2016)
%e A273906 The prime 1013 is a term since 101 and 3 are palindromic.
%e A273906 The prime 101 is not a term, since it is not a concatenation of two nonzero palindromic numbers.
%e A273906 The prime 131 is not a term because it is not a concatenation of two nonzero palindromic numbers.
%t A273906 Take[#, 62] &@ Select[Sort@ Map[FromDigits@ Flatten@ IntegerDigits@ # &, Tuples[#, 2]], PrimeQ] &@ Select[Range[10^3], Reverse@ # == # &@ IntegerDigits@ # &] (* _Michael De Vlieger_, Jun 03 2016 *)
%t A273906 nxtPal[n_]:=With[{c=Join[{2},Flatten[Table[{10*10^d,11*10^d},{d,0,10}]]]},SelectFirst[n+c,PalindromeQ]]; Take[Join[{11},Select[ #[[1]]*10^IntegerLength[ #[[2]]]+#[[2]]&/@ Flatten[{#,Reverse[#]}&/@Subsets[Join[Range[8],NestList[nxtPal,9,100]],{2}],1],PrimeQ]//Union],60] (* _Harvey P. Dale_, Dec 08 2024 *)
%o A273906 (PARI) \\ See program link from _David A. Corneth_, Jun 10 2016.
%Y A273906 Cf. A000040, A002113, A004022, A014950, A096489, A249647, A273906.
%K A273906 nonn,easy,base
%O A273906 1,1
%A A273906 _Giovanni Teofilatto_, Jun 03 2016
%E A273906 More terms from _Michael De Vlieger_, Jun 03 2016