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 A048269 First palindrome greater than n+2 in bases n+2 and n. 3
 5, 26, 21, 24, 154, 40, 121, 60, 181, 84, 253, 112, 337, 144, 433, 180, 541, 220, 661, 264, 793, 312, 937, 364, 1093, 420, 1261, 480, 1441, 544, 1633, 612, 1837, 684, 2053, 760, 2281, 840, 2521, 924, 2773, 1012, 3037, 1104, 3313, 1200, 3601, 1300, 3901 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS a(2), a(3), a(4) and a(6) must be found explicitly. LINKS Colin Barker, Table of n, a(n) for n = 2..1000 Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1). FORMULA 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). n odd and n >= 5: a(n) = (n+3)/2*n+(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). From Colin Barker, Jun 30 2019: (Start) 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). a(n) = (5 + (-1)^(1 + n) + 2*(5 + (-1)^n)*n + 2*(2 + (-1)^n)*n^2) / 4 for n>6. a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>10. (End) EXAMPLE a(15)= (15+3)/2*15+(15+3)/2=144, which is (99) in base 15 and (88) in base 17. MATHEMATICA 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} ] PROG (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 CROSSREFS Cf. A048268. Sequence in context: A057688 A259207 A300005 * A073069 A042281 A041625 Adjacent sequences:  A048266 A048267 A048268 * A048270 A048271 A048272 KEYWORD nonn,easy,base AUTHOR Ulrich Schimke (ulrschimke(AT)aol.com) EXTENSIONS More terms from Robert G. Wilson v, Aug 15 2000 STATUS approved

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Last modified February 20 15:36 EST 2020. Contains 332078 sequences. (Running on oeis4.)