A064737 Fibonacci sequence (A000045) mod 10 with carry.

0, 1, 1, 2, 3, 5, 8, 3, 2, 6, 8, 4, 3, 8, 1, 10, 1, 2, 4, 6, 0, 7, 7, 4, 2, 7, 9, 6, 6, 3, 10, 3, 4, 8, 2, 1, 4, 5, 9, 4, 4, 9, 3, 3, 7, 0, 8, 8, 6, 5, 2, 8, 0, 9, 9, 8, 8, 7, 6, 4, 1, 6, 7, 3, 1, 5, 6, 1, 8, 9, 7, 7, 5, 3, 9, 2, 2, 5, 7, 2, 10, 2, 3, 6, 9, 5, 5, 1, 7, 8, 5, 4, 10, 4, 5, 10, 5, 6, 2, 9, 1, 1

Offset: 0

Author

Robert G. Wilson v, Oct 17 2001

Keywords

• easy
• nonn

Comments

Observation (from Kaprekar) this sequence can be the reverse of 1/109 (A021113) which is recurring and has a period of 108 digits:

0.[009174311926605504587155963302752293577981651376146788\

990825688073394495412844036697247706422018348623853211]. - Eric Desbiaux, Oct 28 2008

Links

• Primes.utm.edu, Sum of 11^n*10^n [From _Eric Desbiaux_, Oct 28 2008]

Crossrefs

Cf. A000045.

Programs

Mathematica

f[0] = 0; f[1] = f[2] = 1; f[n_] := f[n] = Block[{k}, If[f[n - 2] + f[n - 3] >= 10, k = 1, k = 0]; Mod[f[n - 1] + f[n - 2], 10] + k]; Table[ f[n], {n, 0, 100} ]