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 A002477 Wonderful Demlo numbers: a(n) = ((10^n - 1)/9)^2. (Formerly M5386 N2339) 36
 1, 121, 12321, 1234321, 123454321, 12345654321, 1234567654321, 123456787654321, 12345678987654321, 1234567900987654321, 123456790120987654321, 12345679012320987654321, 1234567901234320987654321 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Only the first nine terms of this sequence are palindromes. - Bui Quang Tuan, Mar 30 2015 Not all of the terms are Demlo numbers as defined by Kaprekar, i.e., concat(L,M,R) with M and L+R repdigits using the same digit. For example, a(10), a(19), a(28) are not, but a(k) for k = 11, 12, ..., 18 are. - M. F. Hasler, Nov 18 2017 REFERENCES D. R. Kaprekar, On Wonderful Demlo numbers, Math. Stud., 6 (1938), 68. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..300 Lubomira Dvorakova, Stanislav Kruml, and David Ryzak, Antipalindromic numbers, arXiv:2008.06864 [math.CO], 2020. [Mentions this sequence.] K. R. Gunjikar and D. R. Kaprekar, Theory of Demlo numbers, J. Univ. Bombay, Vol. VIII, Part 3, Nov. 1939, pp. 3-9. [Annotated scanned copy] Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 Eric Weisstein's World of Mathematics, Demlo Number Eric Weisstein's World of Mathematics, Repunit Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000). FORMULA G.f.: x*(1+10*x) / ((1-x)*(1-10*x)*(1-100*x)). - Simon Plouffe in his 1992 dissertation a(n+1) = 100*a(n) + 20*A000042(n) + 1; a(1) = 1. - Reinhard Zumkeller, May 31 2010 a(n) = A000042(n)^2. a(n) = A075412(n)/9 = A178630(n)/18 = A178631(n)/27 = A075415(n)/36 = A178632(n)/45 = A178633(n)/54 = A178634(n)/63 = A178635(n)/72 = A059988(n)/81. - Reinhard Zumkeller, May 31 2010 a(n+2) = -1000*a(n)+110*a(n+1)+11. - Alexander R. Povolotsky, Jun 06 2014 EXAMPLE From José de Jesús Camacho Medina, Apr 01 2016: (Start) n=1: ....................... 1 = 9 / 9; n=2: ..................... 121 = 1089 / 9; n=3: ................... 12321 = 110889 / 9; n=4: ................. 1234321 = 11108889 / 9; n=5: ............... 123454321 = 1111088889 / 9; n=6: ............. 12345654321 = 111110888889 / 9; n=7: ........... 1234567654321 = 11111108888889 / 9; n=8: ......... 123456787654321 = 1111111088888889 / 9; n=9: ....... 12345678987654321 = 111111110888888889 / 9. (End) a(11) = concat(L = 1234567901, R = 20987654321), with L + R = 22222222222 = 2*(10^11-1)/9, of same length as R. - M. F. Hasler, Nov 23 2017 MAPLE A002477 := proc(n) (10^n-1)^2/81 ; end proc: seq(A002477(n), n=1..12) ; # R. J. Mathar, Aug 06 2019 MATHEMATICA Table[FromDigits[PadRight[{}, n, 1]]^2, {n, 15}] (* Harvey P. Dale, Oct 16 2012 *) PROG (PARI) a(n) = (10^n\9)^2 \\ Charles R Greathouse IV, Jul 25 2011 (Magma) [((10^n - 1)/9)^2: n in [1..20]]; // Vincenzo Librandi, Jul 26 2011 (Maxima) A002477(n):=((10^n - 1)/9)^2\$ makelist(A002477(n), n, 1, 10); /* Martin Ettl, Nov 12 2012 */ CROSSREFS Cf. A002275, A080151. Sequence in context: A062689 A057139 A321687 * A173426 A261570 A068117 Adjacent sequences: A002474 A002475 A002476 * A002478 A002479 A002480 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS Minor edits from N. J. A. Sloane, Aug 18 2009 Further edits from Reinhard Zumkeller, May 12 2010 STATUS approved

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Last modified December 3 09:12 EST 2023. Contains 367539 sequences. (Running on oeis4.)