1,1

Numbers n>9 with following property: form a sequence whose initial terms are the t digits of n, later terms given by rule b(i)=sum of t previous terms; then n itself appears in the sequence.

M. Keith, Repfigit Numbers, J. Recreational Math., Vol. 19, No. 2, pp. 41-42, 1987.

C. A. Pickover, All Known Replicating Fibonacci Digits Less Than One Billion, J. Recreational Math., Vol. 22, No. 3, p. 176, 1990.

C. A. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 229.

C. A. Pickover, Wonders of Numbers, "Looping Replicating Fibonacci digits", pp. 174-5, OUP 2000.

K. Sherriff, Computing Replicating Fibonacci Digits, J. Recreational Math., Vol. 26, No. 3, p. 191, 1994.

Also J. Rec. Math., vol. 21, no. 4, p. 310, 1989.

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, see p. 71.

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 197, p. 59, Ellipses, Paris 2008.

N. J. A. Sloane, Table of n, a(n) for n = 1..94 [Taken from first Keith link below.]

M. Keith, Keith numbers

M. Keith, Determination of All Keith Numbers Up to 10^19.

M. Klazar and F. Luca, Counting Keith numbers

Madras Math's Amazing Number Facts, Repfigits

C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Wikipedia, Keith number

197 is a term since sequence is 1, 9, 7, 17, 33, 57, 107, 197, ..., which contains 197.

Cf. A006576, A048970, A050235. See A130010 for another version.

Adjacent sequences: A007626 A007627 A007628 this_sequence A007630 A007631 A007632

Sequence in context: A120158 A130792 A121235 this_sequence A092768 A006576 A083247

nonn,base,nice

njas, Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)

12th term corrected from 2508 to 2580 Aug 15 1997. More terms from Mike Keith (Domnei(AT)aol.com) Feb 15 1999.