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 A048269 #14 May 12 2025 18:24:11
%S A048269 5,26,21,24,154,40,121,60,181,84,253,112,337,144,433,180,541,220,661,
%T A048269 264,793,312,937,364,1093,420,1261,480,1441,544,1633,612,1837,684,
%U A048269 2053,760,2281,840,2521,924,2773,1012,3037,1104,3313,1200,3601,1300,3901
%N A048269 First palindrome greater than n+2 in bases n+2 and n.
%C A048269 a(2), a(3), a(4) and a(6) must be found explicitly.
%H A048269 Colin Barker, <a href="/A048269/b048269.txt">Table of n, a(n) for n = 2..1000</a>
%H A048269 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A048269 n even and n >= 8: a(n) = n^2+(n/2+3)*n+1 (which is (1 n/2+3 1) in base n and (1 n/2-2 1) in base n+2).
%F A048269 n odd and n >= 5: a(n) = (n+1)*(n+3)/2 (which is ((n+3)/2 (n+3)/2) in base n and ((n+1)/2 (n+1)/2) in base n+2).
%F A048269 From _Colin Barker_, Jun 30 2019: (Start)
%F A048269 G.f.: x^2*(5 + 26*x + 6*x^2 - 54*x^3 + 106*x^4 + 46*x^5 - 283*x^6 - 14*x^7 + 259*x^8 - 81*x^10) / ((1 - x)^3*(1 + x)^3).
%F A048269 a(n) = (5 + (-1)^(1 + n) + 2*(5 + (-1)^n)*n + 2*(2 + (-1)^n)*n^2) / 4 for n>6.
%F A048269 a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>10.
%F A048269 (End)
%e A048269 a(15)= (15+3)/2*15+(15+3)/2=144, which is (99) in base 15 and (88) in base 17.
%t A048269 Do[ k = n + 3; While[ RealDigits[ k, n + 2 ][[ 1 ] ] != Reverse[ RealDigits[ k, n + 2 ][[ 1 ] ] ] || RealDigits[ k, n ][[ 1 ] ] != Reverse[ RealDigits[ k, n ][[ 1 ] ] ], k++ ]; Print[ k ], {n, 2, 50} ]
%t A048269 LinearRecurrence[{0,3,0,-3,0,1},{5,26,21,24,154,40,121,60,181,84,253},50] (* _Harvey P. Dale_, May 12 2025 *)
%o A048269 (PARI) Vec(x^2*(5 + 26*x + 6*x^2 - 54*x^3 + 106*x^4 + 46*x^5 - 283*x^6 - 14*x^7 + 259*x^8 - 81*x^10) / ((1 - x)^3*(1 + x)^3) + O(x^50)) \\ _Colin Barker_, Jun 30 2019
%Y A048269 Cf. A048268.
%K A048269 nonn,easy,base
%O A048269 2,1
%A A048269 Ulrich Schimke (ulrschimke(AT)aol.com)
%E A048269 More terms from _Robert G. Wilson v_, Aug 15 2000