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A243063 Numbers generated by a Fibonacci-like sequence in which zeros are suppressed. 5
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 61, 438, 499, 937, 1436, 2373, 389, 2762, 3151, 5913, 964, 6877, 7841, 14718, 22559, 37277, 59836, 97113, 156949, 25462, 182411, 27873, 21284, 49157, 7441, 56598, 6439, 6337, 12776, 19113, 31889, 512, 3241 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Let x(1) = 1, x(2) = 1, then begin the sequence x(i) = no-zero(x(i-2) + x(i-1)), where the function no-zero(n) removes all zero digits from n.

The sequence behaves like a standard Fibonacci sequence until step 15, where x = no-zero(233 + 377) = no-zero(610) = 61. At step 16, x = 377 + 61 = 438. The sequence then proceeds until step 927, where x = no-zero(224 + 377) = no-zero(601) = 61. Therefore at step 928, x = 377 + 61 = 438 and the sequence repeats.

LINKS

Anthony Sand, Table of n, a(n) for n = 1..927

FORMULA

x(i) = no-zero(x(i-2) + x(i-1)). For example, no-zero(233 + 377) = no-zero(610) = 61.

EXAMPLE

x(3) = x(1) + x(2) = 1 + 1 = 2.

x(4) = x(2) + x(3) = 1 + 2 = 3.

x(15) = no-zero(x(13) + x(14)) = no-zero(233 + 377) = no-zero(610) = 61.

x(16) = 377 + 61 = 438.

MAPLE

noz:=proc(n) local a, t1, i, j; a:=0; t1:=convert(n, base, 10); for i from 1 to nops(t1) do j:=t1[nops(t1)+1-i]; if j <> 0 then a := 10*a+j; fi; od: a; end; # A004719

t1:=[1, 1]; for n from 3 to 100 do t1:=[op(t1), noz(t1[n-1]+t1[n-2])]; od: t1; # N. J. A. Sloane, Jun 11 2014

CROSSREFS

Cf. A000045, A004719, A242350, A243657, A243658, A306773.

Sequence in context: A023442 A000044 A107358 * A248740 A185357 A132636

Adjacent sequences:  A243060 A243061 A243062 * A243064 A243065 A243066

KEYWORD

nonn,base

AUTHOR

Anthony Sand, Jun 09 2014

STATUS

approved

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Last modified December 7 20:30 EST 2019. Contains 329849 sequences. (Running on oeis4.)