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 A006960 Reverse and Add! sequence starting with 196. (Formerly M5410) 46
 196, 887, 1675, 7436, 13783, 52514, 94039, 187088, 1067869, 10755470, 18211171, 35322452, 60744805, 111589511, 227574622, 454050344, 897100798, 1794102596, 8746117567, 16403234045, 70446464506, 130992928913, 450822227944, 900544455998, 1800098901007, 8801197801088, 17602285712176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 196 is conjectured to be the smallest initial term which does not lead to a palindrome. John Walker, Tim Irvin and others have extended the trajectory of 196 to millions of digits without finding a palindrome. From A.H.M. Smeets, Jan 31 2019: (Start) Palindromes for a(9)/2, a(14)/2 and a(20)/2. Observed:  It seems that most, but not all, Lychrel numbers (seeds given in A063048) have a trajectory term that, divided by 2, becomes palindromic. Note that 196 is the first Lychrel number (A063048(1)). (End) Observed: On average, 0.414 digits are gained by each step of the reverse and add procedure; i.e., 2.416 steps are needed on average to gain a factor of 10. This holds for any trajectory of reverse and add for decimal number representation. - A.H.M. Smeets, Feb 03 2019 REFERENCES J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 196, p. 58, Ellipses, Paris 2008. F. Gruenberger, Computer Recreations, Scientific American, 250 (No. 4, 1984), 19-26. D. H. Lehmer, "Sujets d'étude. No. 74," Sphinx (Bruxelles), 8 (1938), 12-13. (This is the currently earliest known reference to the 196 Problem). -  James D. Klein, Apr 09 2012. Daniel Lignon, Dictionnaire de (presque) tous les nombres entiers, Ellipses, Paris, 2012, 702 pages. See Entry 196. Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 70. Popular Computing (Calabasas, CA), The 196 Problem, Vol. 3 (No. 30, Sep 1975), pages PC30-6 to PC30-9. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe and Michael Lee, Table of n, a(n) for n = 0..2390 (T. D. Noe supplied terms 0 to 200) Patrick De Geest, Some thematic websources Jason Doucette, World Records Martianus Frederic Ezerman, Bertrand Meyer and Patrick Sole, On Polynomial Pairs of Integers, arXiv:1210.7593 [math.NT], 2012. - From N. J. A. Sloane, Nov 08 2012 Felix Fröhlich, C++ program for this sequence R. K. Guy, What's left?, Math Horizons, Vol. 5, No. 4 (April 1998), pp. 5-7. Madras Math's Amazing Number Facts, The Ultimate Palindrome I. Peter, More trajectories Wade VanLandingham, 196 and Other Lychrel Numbers Eric Weisstein's World of Mathematics, 196-Algorithm. Eric Weisstein's World of Mathematics, Palindromic Number Conjecture. FORMULA a(n+1) = A056964(a(n)). - A.H.M. Smeets, Jan 27 2019 EXAMPLE From M. F. Hasler, Apr 13 2019: (Start) Start with 196 = a(0), then: A056964(196) = 196 + 691 = 887 = a(1); then: A056964(887) = 887 + 788 = 1675 = a(2); then: A056964(1675) = 1675 + 5761 = 7436 = a(3); then: A056964(7436) = 7436 + 6347 = 13783 = a(4); then: A056964(13783) = 13783 + 38731 = 52514 = a(5); etc. (End) MAPLE a:= proc(n) option remember; `if`(n=0, 196, (h-> h+ (s->       parse(cat(s[-i]\$i=1..length(s))))(""||h))(a(n-1)))     end: seq(a(n), n=0..40);  # Alois P. Heinz, Jul 25 2014 MATHEMATICA a = {196}; For[i = 2, i < 26, i++, a = Append[a, a[[i - 1]] + ToExpression[ StringReverse[ToString[a[[i - 1]]]]]]]; a NestList[#+FromDigits[Reverse[IntegerDigits[#]]]&, 196, 25] (* Harvey P. Dale, Jun 05 2011 *) NestList[#+IntegerReverse[#]&, 196, 25] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 04 2019 *) PROG (Haskell) a006960 n = a006960_list !! n a006960_list = iterate a056964 196 -- Reinhard Zumkeller, Sep 22 2011 (PARI) A006960_vec(N=99)=vector(N, i, N=if(i>1, A056964(N), 196)) \\ M. F. Hasler, Apr 13 2019 CROSSREFS Cf. A023108, A023109, A033665, A016016, A056964, A004086. Sequence in context: A088753 A063048 A306232 * A014798 A251308 A251301 Adjacent sequences:  A006957 A006958 A006959 * A006961 A006962 A006963 KEYWORD nonn,base,nice,easy AUTHOR EXTENSIONS More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 28 2002 STATUS approved

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Last modified April 17 15:33 EDT 2021. Contains 343063 sequences. (Running on oeis4.)