A006960 - OEIS (original) (raw)

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

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.

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.

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

R. K. Guy, What's left?, Math Horizons, Vol. 5, No. 4 (April 1998), pp. 5-7.

EXAMPLE

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:

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

EXTENSIONS

More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 28 2002